1312:
84:
3913:
46:
1720:) arguing along the lines that the short lifetime of virtual particles allows the "borrowing" of large energies from the vacuum and thus permits particle generation for short times. Although the phenomenon of virtual particles is accepted, this interpretation of the energy-time uncertainty relation is not universal. One issue is the use of an uncertainty relation limiting measurement accuracy as though a time uncertainty Î
1795:(1994): "... all quantum fields have zero-point energies and vacuum fluctuations." This means that there is a component of the quantum vacuum respectively for each component field (considered in the conceptual absence of the other fields), such as the electromagnetic field, the Dirac electron-positron field, and so on. According to Milonni (1994), some of the effects attributed to the
1317:
1316:
1313:
1318:
1315:
1803:
between uncharged conductive plates is often proposed as an example of an effect of the vacuum electromagnetic field. Schwinger, DeRaad, and Milton (1978) are cited by
Milonni (1994) as validly, though unconventionally, explaining the Casimir effect with a model in which "the vacuum is regarded as
1808:
The basic idea here will be that the
Casimir force may be derived from the source fields alone even in completely conventional QED, ... Milonni provides detailed argument that the measurable physical effects usually attributed to the vacuum electromagnetic field cannot be explained by that field
1809:
alone, but require in addition a contribution from the self-energy of the electrons, or their radiation reaction. He writes: "The radiation reaction and the vacuum fields are two aspects of the same thing when it comes to physical interpretations of various QED processes including the
1751:). Various schemes have been advanced to construct an observable that has some kind of time interpretation, and yet does satisfy a canonical commutation relation with energy. Many approaches to the energy-time uncertainty principle are a long and continuing subject.
1636:" refers to the variance of the field strength in the minimal energy state, and is described picturesquely as evidence of "virtual particles". It is sometimes attempted to provide an intuitive picture of virtual particles, or variances, based upon the Heisenberg
1314:
1214:
According to present-day understanding of what is called the vacuum state or the quantum vacuum, it is "by no means a simple empty space". According to quantum mechanics, the vacuum state is not truly empty but instead contains fleeting
1804:
truly a state with all physical properties equal to zero." In this model, the observed phenomena are explained as the effects of the electron motions on the electromagnetic field, called the source field effect. Milonni writes:
1821:
This point of view is also stated by Jaffe (2005): "The
Casimir force can be calculated without reference to vacuum fluctuations, and like all other observable effects in QED, it vanishes as the fine structure constant,
1498:
Quantum corrections to
Maxwell's equations are expected to result in a tiny nonlinear electric polarization term in the vacuum, resulting in a field-dependent electrical permittivity Δ deviating from the nominal value
2492:
Davis; Harris, Joseph; Gammon; Smolyaninov; Kyuman Cho (2007). "Experimental
Challenges Involved in Searches for Axion-Like Particles and Nonlinear Quantum Electrodynamic Effects by Sensitive Optical Techniques".
1684:
1787:
Photon-photon interaction can occur only through interaction with the vacuum state of some other field, such as the Dirac electron-positron vacuum field; this is associated with the concept of
1957:
1588:
2684:
This "borrowing" idea has led to proposals for using the zero-point energy of vacuum as an infinite reservoir and various "camps" about this interpretation. See, for example,
1602:
from particle physics, outside quantum electrodynamics, also have been proposed. Experimentally measuring such an effect is challenging, and has not yet been successful.
1862:
1887:
2716:
Quantities satisfying a canonical commutation rule are noncompatible observables, meaning they can both be measured simultaneously, only with limited precision. See
1915:
2395:
3157:
1783:
It is impossible by any procedure, no matter how idealized, to reduce any assembly to the absolute zero in a finite number of operations. (See also.)
3710:
1643:
2431:
Gies, Holger; Jaeckel, Joerg; Ringwald, Andreas (2006). "Polarized Light
Propagating in a Magnetic Field as a Probe of Millicharged Fermions".
1170:
3130:
3358:
253:
1637:
3881:
3102:
Puthoff, H. E.; Little, S. R.; Ibison, M. (2001). "Engineering the Zero-Point Field and
Polarizable Vacuum for Interstellar Flight".
1621:
293:
3207:
3893:
1335:
1412:, and this zero-point energy (equivalent to the lowest possible energy state) has measurable effects. It may be detected as the
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3150:
1327:
3511:
2828:
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2731:
2701:
2658:
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2589:
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2142:
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2207:
2091:
3434:
2065:
1028:
1519:
so that in the presence of a very strong electric field, the permittivity is increased by a tiny amount with respect to Δ
1557:
A characteristic electric field strength for which the nonlinearities become sizable is predicted to be enormous, about
2237:
2035:
1163:
2669:. This implies that the amplitude for the total energy involved in the interaction is spread over a range of energies
3180:
3143:
3082:
3033:
2977:
2956:
2935:
2914:
1523:. Subject to ongoing experimental efforts is the possibility that a strong electric field would modify the effective
1379:
3290:
1763:(2002): "When one empties out a space of all matter and lowers the temperature to absolute zero, one produces in a
798:
2928:
The Theory of
Photons and Electrons. The Relativistic Quantum Field Theory of Charged Particles with Spin One-half
3848:
3557:
3552:
3275:
1554:
1549:
for an electromagnetic wave traveling in a direction other than the electric field. The effect is similar to the
1290:
96:
31:
2793:(2008). "Chapter 3: The TimeâEnergy Uncertainty Relation". In J.G. Muga; R. Sala Mayato; Ă.L. Egusquiza (eds.).
3860:
3532:
1920:
1741:
1424:. The energy of a cubic centimeter of empty space has been calculated figuratively to be one trillionth of an
3937:
3838:
3615:
3537:
3320:
3190:
1473:
1391:
1156:
361:
210:
170:
1362:
vanishes. For quantum field theories in which perturbation theory breaks down at low energies (for example,
1238:
to be developed. QED originated in the 1930s, and in the late 1940s and early 1950s, it was reformulated by
3572:
3506:
3501:
3472:
3185:
1432:
is that the energy of the quantum vacuum state must explain the physically observed cosmological constant.
1359:
898:
828:
200:
17:
1472:
of the field theory. In this case, the vacuum has less symmetry than the theory allows, and one says that
3640:
3547:
1776:
1211:
is sometimes used as a synonym for the vacuum state of a quantized field which is completely individual.
356:
298:
1560:
3916:
3678:
3486:
3457:
3116:
E. W. Davis, V. L. Teofilo, B. Haisch, H. E. Puthoff, L. J. Nickisch, A. Rueda and D. C. Cole (2006), "
1524:
205:
1008:
3700:
3567:
3491:
3452:
3409:
3383:
3340:
3233:
1469:
346:
2860:
Statistical
Thermodynamics. A Version of Statistical Mechanics for Students of Physics and Chemistry
3767:
3747:
3737:
3727:
3683:
3258:
3070:
1890:
1728:. Another issue is the meaning of "time" in this relation because energy and time (unlike position
1598:
has been estimated, being about 10 times smaller than the Kerr constant of water. Explanations for
1461:
1457:
1375:
1355:
1306:
833:
463:
308:
273:
2185:
823:
3947:
3462:
3388:
1989:
1717:
1508:
1507:. These theoretical developments are described, for example, in Dittrich and Gies. The theory of
1259:
1231:
1108:
578:
386:
381:
243:
3876:
3424:
2618:
1839:
1553:
but without matter being present. This tiny nonlinearity can be interpreted in terms of virtual
3787:
3562:
3542:
3467:
3335:
2790:
2747:
2719:
2596:
The spontaneous, temporary emergence of particles from vacuum is called a "vacuum fluctuation".
2579:
2160:
1867:
1363:
1274:
978:
958:
458:
391:
303:
268:
27:
Lowest-energy state of a field in quantum field theories, corresponding to no particles present
3378:
2759:
2687:
2644:
2552:
2518:
3812:
3325:
3305:
2328:
Battesti, RĂ©my; et al. (November 2018). "High magnetic fields for fundamental physics".
2132:
1421:
1286:
1216:
868:
728:
424:
288:
150:
2751:
1452:
but can also be proved directly without these axioms. Poincaré invariance implies that only
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3772:
3717:
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3228:
2999:
2855:
2808:
2450:
2343:
2273:
1900:
1772:
1441:
1429:
1235:
1184:
1113:
893:
429:
283:
75:
65:
1445:
195:
8:
3828:
3797:
3742:
3722:
3630:
3587:
3442:
3368:
3295:
3285:
3197:
3053:
2004:
1994:
1814:
1788:
1633:
1545:
in the perpendicular direction. The quantum vacuum exposed to an electric field exhibits
1504:
1465:
1351:
1343:
1323:
1294:
1270:
1123:
453:
3003:
2812:
2454:
2347:
2277:
838:
568:
3888:
3757:
3655:
3363:
3310:
3202:
3117:
3103:
2834:
2798:
2611:
2494:
2474:
2440:
2359:
2333:
2308:
2289:
2263:
2034:
Lambrecht, Astrid (2002). Figger, Hartmut; Meschede, Dieter; Zimmermann, Claus (eds.).
1999:
1984:
1417:
1278:
1243:
1133:
1058:
988:
873:
858:
788:
753:
743:
703:
618:
508:
468:
258:
220:
175:
163:
140:
135:
3898:
3807:
3777:
3705:
3668:
3663:
3645:
3610:
3600:
3315:
3280:
3263:
3166:
3078:
3029:
3011:
2990:
Schwinger, J.; DeRaad, L. L.; Milton, K. A. (1978). "Casimir effect in dielectrics".
2973:
2952:
2931:
2910:
2824:
2797:. Lecture Notes in Physics. Vol. 734 (2nd ed.). Springer. pp. 73â105.
2766:
2752:
2727:
2697:
2654:
2622:
2585:
2558:
2524:
2466:
2408:
2285:
2217:
2172:
2138:
2071:
2044:
2037:
Observing mechanical dissipation in the quantum vacuum: an experimental challenge; in
1409:
1371:
1088:
1018:
903:
748:
683:
653:
623:
483:
478:
323:
248:
238:
130:
39:
2838:
2478:
2377:
2293:
808:
3625:
3620:
3477:
3373:
3007:
2816:
2458:
2363:
2351:
2281:
1799:
can have several physical interpretations, some more conventional than others. The
1792:
1760:
1611:
1516:
1453:
1255:
1251:
1247:
1128:
1043:
1023:
993:
943:
768:
763:
758:
643:
628:
558:
263:
190:
180:
115:
2862:, reprinted with corrections, Cambridge University Press, London, England, p. 224.
2462:
2355:
3942:
3855:
3782:
3762:
3732:
3695:
3690:
3595:
3419:
3074:
2514:
2095:
1969:
1591:
1493:
1477:
1449:
1239:
1073:
1068:
1038:
1033:
1003:
963:
933:
913:
818:
713:
708:
673:
658:
633:
613:
593:
523:
513:
434:
396:
313:
278:
110:
88:
83:
2820:
2689:
Quest for zero point energy: engineering principles for 'free energy' inventions
3833:
3802:
3792:
3414:
3404:
3238:
2010:
1800:
1481:
1413:
1383:
1266:
1098:
1048:
968:
953:
938:
918:
888:
883:
878:
863:
848:
813:
803:
733:
668:
638:
573:
538:
528:
503:
374:
341:
215:
853:
3931:
3752:
3605:
3496:
3330:
3300:
3253:
1974:
1595:
1546:
1403:
1200:
1103:
1093:
1083:
1078:
998:
983:
783:
778:
608:
603:
563:
533:
498:
488:
419:
414:
61:
3635:
3248:
3243:
2851:
2470:
1768:
1347:
1339:
1338:, then the properties of the vacuum are analogous to the properties of the
1138:
1063:
948:
923:
908:
843:
723:
718:
598:
588:
583:
548:
543:
518:
473:
351:
318:
145:
125:
49:
1285:
is the vacuum of quantum chromodynamics. It is the object of study in the
3673:
3108:
2803:
2183:
For the Nobel prize details and the Nobel lectures by these authors, see
1550:
1528:
1394:, is the mechanism by which the other fields in the theory acquire mass.
1387:
1250:, who jointly received the Nobel prize for this work in 1965. Today, the
1118:
1053:
1013:
973:
928:
793:
698:
693:
678:
663:
648:
2746:
2254:
Bednorz, Adam (November 2013). "Relativistic invariance of the vacuum".
2445:
2313:
1979:
1810:
1796:
1617:
1512:
1367:
1282:
1227:
773:
688:
553:
493:
185:
120:
2750:; Marian Grabowski; Pekka J. Lahti (1995). "§III.4: Energy and time".
3527:
3223:
3118:
Review of
Experimental Concepts for Studying the Quantum Vacuum Field
2535:
For all field states that have classical analog the field quadrature
2115:
1599:
3135:
68:, the ground state is usually called the vacuum state or the vacuum.
2536:
2338:
1629:
1616:
The presence of virtual particles can be rigorously based upon the
1220:
738:
53:
2499:
2268:
2134:
Probing the quantum vacuum: perturbative effective action approach
1625:
2888:
Wilks, J. (1971). The Third Law of Thermodynamics, Chapter 6 in
1334:
If the quantum field theory can be accurately described through
45:
2307:
Delphenich, David (2006). "Nonlinear Electrodynamics and QED".
2241:
1695:
1428:(or 0.6 eV). An outstanding requirement imposed on a potential
1204:
35:
3026:
The Quantum Vacuum. An Introduction to Quantum Electrodynamics
2970:
The Quantum Vacuum. An Introduction to Quantum Electrodynamics
2949:
The Quantum Vacuum. An Introduction to Quantum Electrodynamics
2892:, volume 1, ed. W. Jost, of H. Eyring, D. Henderson, W. Jost,
1538:
in the direction of the electric field and slightly exceeding
1277:(or QCD) is the portion of the Standard Model that deals with
1258:
are unified (at very high energies only) in the theory of the
30:
This article is about the quantum vacuum. For other uses, see
2043:. Berlin, Germany/New York, New York: Springer. p. 197.
1269:
is a generalization of the QED work to include all the known
3045:
Jaffe, R. L. (2005). Casimir effect and the quantum vacuum,
2581:
Cosmic Understanding: Philosophy and Science of the Universe
2491:
2165:
Historical Encyclopedia of Natural and Mathematical Sciences
2244:
broadcast of Cosmology at Yearly Kos Science Panel, Part 1.
1699:
1679:{\displaystyle \Delta E\Delta t\geq {\frac {\hbar }{2}}\,,}
57:
2327:
1425:
1207:. Generally, it contains no physical particles. The term
1754:
3028:, Academic Press, Incorporated, Boston, Massachusetts,
2972:, Academic Press, Incorporated, Boston, Massachusetts,
2951:, Academic Press, Incorporated, Boston, Massachusetts,
2879:, Longmans, Green and Company, London, England, p. 220.
1628:
values of the fields vanish in a quantum vacuum, their
1420:, the energy of the cosmological vacuum appears as the
3054:
http://1â5.cua.mit.edu/8.422_s07/jaffe2005_casimir.pdf
2930:, second expanded edition, Springer-Verlag, New York,
2167:. Vol. 1 (5th ed.). Springer. pp. 4892
1293:, and is related to the so-called vacuum structure of
2989:
1923:
1903:
1870:
1842:
1646:
1563:
3101:
2430:
1456:combinations of field operators have non-vanishing
2720:"§ 351 (XX.23) C: Canonical commutation relations"
2610:
2539:are also greater than or equal to this commutator.
2070:. London/New York: Routledge. Chapter 10, p. 205.
1951:
1909:
1881:
1856:
1706:is the accuracy in the measurement of energy and Î
1678:
1582:
2665:The interaction will last for a certain duration
2205:
3929:
2877:Fundamental Principles. The Properties of Gases
2642:
2608:
2236:Sean Carroll, Sr Research Associate â Physics,
2158:
1386:, the non-zero vacuum expectation value of the
3071:The Structured Vacuum â thinking about nothing
3151:
2685:
2376:Mourou, G. A.; T. Tajima, and S. V. Bulanov,
2157:For a historical discussion, see for example
1300:
1164:
2513:
2130:
1946:
1924:
1876:
1851:
1724:determines a "budget" for borrowing energy Î
1223:that pop into and out of the quantum field.
34:. For the classical notion of a vacuum, see
2909:, American Institute of Physics, New York,
2710:
2692:. Adventures Unlimited Press. pp. 124
2584:. Princeton University Press. p. 132.
2029:
2027:
3158:
3144:
2873:An Advanced Treatise on Physical Chemistry
2789:
2717:
2520:Modern nonlinear optics, Volume 85, Part 3
2507:
2306:
2300:
2206:Letessier, Jean; Rafelski, Johann (2002).
2126:
2124:
1710:is the time taken in the measurement, and
1624:. Non-commutation means that although the
1487:
1374:), field operators may have non-vanishing
1171:
1157:
82:
38:. For the related zero-point concept, see
3107:
2802:
2726:(2nd ed.). MIT Press. p. 1303.
2498:
2444:
2337:
2312:
2267:
2212:. Cambridge University Press. p. 37
2033:
1952:{\displaystyle \langle 0|\phi |0\rangle }
1672:
1273:and their interactions (except gravity).
3097:Nothingness: The Science of Empty Space.
2926:Jauch, J. M.; Rohrlich, F. (1955/1980).
2894:Physical Chemistry. An Advanced Treatise
2784:
2782:
2649:(2nd ed.). CRC Press. pp. 224
2247:
2199:
2131:Dittrich, Walter & Gies, H. (2000).
2024:
1779:may be precisely enunciated as follows:
1767:the quantum vacuum state." According to
1310:
44:
3090:An introduction to Quantum Field Theory
2617:. Cambridge University Press. pp.
2550:
2544:
2253:
2121:
14:
3930:
2740:
2724:Encyclopedic dictionary of mathematics
2635:
2601:
2577:
2571:
2523:. John Wiley & Sons. p. 462.
2370:
2151:
1408:The vacuum state is associated with a
1328:spontaneous parametric down-conversion
3165:
3139:
2779:
2557:. Taylor & Francis. p. 126.
1755:Physical nature of the quantum vacuum
2678:
2641:A vaguer description is provided by
1605:
2896:, Academic Press, New York, p. 477.
2551:Klyshko, David Nikolaevich (1988).
2063:
1322:The video of an experiment showing
24:
3088:M. E. Peskin and D. V. Schroeder,
3063:
2238:California Institute of Technology
2057:
1653:
1647:
1583:{\displaystyle 1.32\times 10^{18}}
25:
3959:
3124:
2407:Klein, James J. and B. P. Nigam,
2379:Optics in the relativistic regime
2186:"The Nobel Prize in Physics 1965"
1638:energy-time uncertainty principle
1234:(or QED) was the first vacuum of
3912:
3911:
2646:Quarks, leptons and the big bang
1740:, for example) do not satisfy a
1622:quantized electromagnetic fields
3039:
3018:
2983:
2962:
2941:
2920:
2899:
2882:
2865:
2845:
2485:
2424:
2401:
2321:
2256:The European Physical Journal C
2161:"Quantum electrodynamics (QED)"
2116:Physical Review Focus Dec. 1998
1836:The vacuum state is written as
1326:(in the red ring) amplified by
1291:Relativistic Heavy Ion Collider
32:Quantum vacuum (disambiguation)
3861:Relativistic quantum mechanics
2286:10.1140/epjc/s10052-013-2654-9
2230:
2209:Hadrons and Quark-Gluon Plasma
2109:
2092:"AIP Physics News Update,1996"
2084:
1939:
1931:
1872:
1844:
1742:canonical commutation relation
13:
1:
3839:Quantum statistical mechanics
3616:Quantum differential calculus
3538:Delayed-choice quantum eraser
3321:Symmetry in quantum mechanics
2517:; Kielich, Stanislaw (1994).
2463:10.1103/PhysRevLett.97.140402
2394:(no. 2), pp. 309â371, (2006)
2356:10.1016/j.physrep.2018.07.005
2159:Ari Ben-Menaáž„em, ed. (2009).
2017:
1474:spontaneous symmetry breaking
1392:spontaneous symmetry breaking
211:Spontaneous symmetry breaking
171:Symmetry in quantum mechanics
3012:10.1016/0003-4916(78)90172-0
2554:Photons and nonlinear optics
1831:
1797:vacuum electromagnetic field
1531:with a value slightly below
1444:field theory, the vacuum is
1252:electromagnetic interactions
7:
3641:Quantum stochastic calculus
3631:Quantum measurement problem
3553:MachâZehnder interferometer
2821:10.1007/978-3-540-73473-4_3
2754:Operational quantum physics
2410:Birefringence of the vacuum
2039:Laser physics at the limits
1962:
1777:third law of thermodynamics
1435:
10:
3964:
2907:A Survey of Thermodynamics
2871:Partington, J. R. (1949).
2578:Munitz, Milton K. (1990).
2421:, pp. B1279âB1280, (1964).
2067:Time, space and philosophy
1857:{\displaystyle |0\rangle }
1702:variations respectively; Î
1609:
1525:permeability of free space
1491:
1401:
1346:, or more accurately, the
1304:
1301:Non-zero expectation value
206:Explicit symmetry breaking
29:
3907:
3869:
3821:
3701:Quantum complexity theory
3679:Quantum cellular automata
3654:
3586:
3520:
3433:
3397:
3384:Path integral formulation
3351:
3216:
3173:
3077:and Berndt Muller (1985)
2795:Time in Quantum Mechanics
2388:Reviews of Modern Physics
2064:Ray, Christopher (1991).
1882:{\displaystyle |\rangle }
1397:
1376:vacuum expectation values
1203:with the lowest possible
362:BargmannâWigner equations
3768:Quantum machine learning
3748:Quantum key distribution
3738:Quantum image processing
3728:Quantum error correction
3578:Wheeler's delayed choice
2643:Jonathan Allday (2002).
2609:P. C. W. Davies (1982).
1891:vacuum expectation value
1515:should exhibit a slight
1356:vacuum expectation value
1342:of a quantum mechanical
1307:Vacuum expectation value
3684:Quantum finite automata
3024:Milonni, P. W. (1994).
2968:Milonni, P. W. (1994).
2947:Milonni, P. W. (1994).
2613:The accidental universe
2433:Physical Review Letters
1990:Squeezed coherent state
1817:, and Casimir effects."
1718:Reduced Planck constant
1509:quantum electrodynamics
1488:Non-linear permittivity
1260:electroweak interaction
1232:quantum electrodynamics
387:Electroweak interaction
382:Quantum electrodynamics
357:WheelerâDeWitt equation
244:Background field method
3788:Quantum neural network
2686:Moray B. King (2001).
1953:
1911:
1883:
1858:
1819:
1785:
1680:
1584:
1464:may break some of the
1416:in the laboratory. In
1364:Quantum chromodynamics
1331:
1275:Quantum chromodynamics
392:Quantum chromodynamics
269:Effective field theory
69:
3813:Quantum teleportation
3341:Waveâparticle duality
2856:Guggenheim, Edward A.
2758:. Springer. pp.
1954:
1917:should be written as
1912:
1910:{\displaystyle \phi }
1884:
1859:
1806:
1781:
1681:
1585:
1448:, which follows from
1422:cosmological constant
1321:
1287:Large Hadron Collider
1217:electromagnetic waves
347:KleinâGordon equation
289:LSZ reduction formula
48:
3938:Quantum field theory
3844:Quantum field theory
3773:Quantum metamaterial
3718:Quantum cryptography
3448:Consistent histories
2607:For an example, see
2137:. Berlin: Springer.
1921:
1901:
1868:
1840:
1815:van der Waals forces
1644:
1561:
1430:Theory of Everything
1354:. In this case, the
1271:elementary particles
1236:quantum field theory
1189:quantum vacuum state
1185:quantum field theory
430:Theory of everything
284:Lattice field theory
254:Correlation function
76:Quantum field theory
66:quantum field theory
3829:Quantum fluctuation
3798:Quantum programming
3758:Quantum logic gates
3743:Quantum information
3723:Quantum electronics
3198:Classical mechanics
3004:1978AnPhy.115....1S
2905:Bailyn, M. (1994).
2813:2002tqm..conf...69B
2718:Kiyosi ItĂŽ (1993).
2455:2006PhRvL..97n0402G
2348:2018PhR...765....1B
2278:2013EPJC...73.2654B
2005:Van der Waals force
1995:Quantum fluctuation
1789:vacuum polarization
1634:vacuum fluctuations
1505:vacuum permittivity
1466:internal symmetries
1352:measurement problem
1344:harmonic oscillator
1336:perturbation theory
1324:vacuum fluctuations
1295:strong interactions
1279:strong interactions
409:Incomplete theories
60:: ground state and
3882:in popular culture
3664:Quantum algorithms
3512:Von NeumannâWigner
3492:Objective collapse
3203:Old quantum theory
3131:Energy into Matter
3047:Physical Review D,
2788:For a review, see
2000:Scharnhorst effect
1985:False vacuum decay
1949:
1907:
1879:
1854:
1801:Casimir attraction
1765:Gedankenexperiment
1676:
1632:do not. The term "
1590:V/m, known as the
1580:
1511:predicts that the
1476:has occurred. See
1446:Poincaré invariant
1418:physical cosmology
1332:
294:Partition function
221:Topological charge
141:General relativity
136:Special relativity
70:
3925:
3924:
3899:Quantum mysticism
3877:Schrödinger's cat
3808:Quantum simulator
3778:Quantum metrology
3706:Quantum computing
3669:Quantum amplifier
3646:Quantum spacetime
3611:Quantum cosmology
3601:Quantum chemistry
3316:Scattering theory
3264:Zero-point energy
3259:Degenerate levels
3167:Quantum mechanics
3069:Free pdf copy of
2992:Annals of Physics
2830:978-3-540-73472-7
2772:978-3-540-59358-4
2733:978-0-262-59020-4
2703:978-0-932813-94-7
2660:978-0-7503-0806-9
2628:978-0-521-28692-3
2591:978-0-691-02059-4
2564:978-2-88124-669-2
2530:978-0-471-57548-1
2332:. 765â766: 1â39.
2223:978-0-521-38536-7
2178:978-3-540-68831-0
2144:978-3-540-67428-3
2077:978-0-415-03221-6
2050:978-3-540-42418-5
1895:Expectation value
1828:, goes to zero."
1775:(1939/1965), the
1670:
1606:Virtual particles
1594:; the equivalent
1410:zero-point energy
1372:superconductivity
1319:
1256:weak interactions
1191:(also called the
1181:
1180:
274:Expectation value
249:BRST quantization
196:Poincaré symmetry
151:YangâMills theory
131:Quantum mechanics
40:Zero-point energy
16:(Redirected from
3955:
3915:
3914:
3626:Quantum geometry
3621:Quantum dynamics
3478:Superdeterminism
3374:Matrix mechanics
3229:Braâket notation
3160:
3153:
3146:
3137:
3136:
3113:
3111:
3109:astro-ph/0107316
3057:
3043:
3037:
3022:
3016:
3015:
2987:
2981:
2966:
2960:
2945:
2939:
2924:
2918:
2903:
2897:
2886:
2880:
2869:
2863:
2849:
2843:
2842:
2806:
2804:quant-ph/0105049
2786:
2777:
2776:
2757:
2744:
2738:
2737:
2714:
2708:
2707:
2682:
2676:
2675:
2639:
2633:
2632:
2616:
2605:
2599:
2598:
2575:
2569:
2568:
2548:
2542:
2541:
2515:Evans, Myron Wyn
2511:
2505:
2504:
2502:
2489:
2483:
2482:
2448:
2428:
2422:
2415:Physical Review,
2405:
2399:
2374:
2368:
2367:
2341:
2325:
2319:
2318:
2316:
2304:
2298:
2297:
2271:
2251:
2245:
2240:, June 22, 2006
2234:
2228:
2227:
2203:
2197:
2196:
2194:
2193:
2188:. Nobelprize.org
2182:
2155:
2149:
2148:
2128:
2119:
2113:
2107:
2106:
2104:
2103:
2094:. Archived from
2088:
2082:
2081:
2061:
2055:
2054:
2031:
1958:
1956:
1955:
1950:
1942:
1934:
1916:
1914:
1913:
1908:
1888:
1886:
1885:
1880:
1875:
1863:
1861:
1860:
1855:
1847:
1827:
1761:Astrid Lambrecht
1750:
1739:
1733:
1715:
1685:
1683:
1682:
1677:
1671:
1663:
1612:Virtual particle
1589:
1587:
1586:
1581:
1579:
1578:
1320:
1209:zero-point field
1173:
1166:
1159:
264:Effective action
191:Lorentz symmetry
116:Electromagnetism
86:
72:
71:
21:
3963:
3962:
3958:
3957:
3956:
3954:
3953:
3952:
3928:
3927:
3926:
3921:
3903:
3889:Wigner's friend
3865:
3856:Quantum gravity
3817:
3803:Quantum sensing
3783:Quantum network
3763:Quantum machine
3733:Quantum imaging
3696:Quantum circuit
3691:Quantum channel
3650:
3596:Quantum biology
3582:
3558:ElitzurâVaidman
3533:DavissonâGermer
3516:
3468:Hidden-variable
3458:de BroglieâBohm
3435:Interpretations
3429:
3393:
3347:
3234:Complementarity
3212:
3169:
3164:
3127:
3075:Johann Rafelski
3066:
3064:Further reading
3061:
3060:
3044:
3040:
3023:
3019:
2988:
2984:
2967:
2963:
2946:
2942:
2925:
2921:
2904:
2900:
2887:
2883:
2870:
2866:
2850:
2846:
2831:
2787:
2780:
2773:
2745:
2741:
2734:
2715:
2711:
2704:
2683:
2679:
2661:
2640:
2636:
2629:
2606:
2602:
2592:
2576:
2572:
2565:
2549:
2545:
2531:
2512:
2508:
2490:
2486:
2429:
2425:
2406:
2402:
2375:
2371:
2330:Physics Reports
2326:
2322:
2305:
2301:
2252:
2248:
2235:
2231:
2224:
2204:
2200:
2191:
2189:
2184:
2179:
2156:
2152:
2145:
2129:
2122:
2114:
2110:
2101:
2099:
2090:
2089:
2085:
2078:
2062:
2058:
2051:
2032:
2025:
2020:
2015:
1970:Pair production
1965:
1938:
1930:
1922:
1919:
1918:
1902:
1899:
1898:
1897:) of any field
1871:
1869:
1866:
1865:
1843:
1841:
1838:
1837:
1834:
1823:
1791:. According to
1757:
1745:
1735:
1729:
1711:
1662:
1645:
1642:
1641:
1618:non-commutation
1614:
1608:
1592:Schwinger limit
1574:
1570:
1562:
1559:
1558:
1555:pair production
1544:
1537:
1522:
1502:
1496:
1494:Schwinger limit
1490:
1478:Higgs mechanism
1450:Wightman axioms
1438:
1406:
1400:
1390:, arising from
1311:
1309:
1303:
1177:
1148:
1147:
1146:
1144:
448:
440:
439:
435:Quantum gravity
410:
402:
401:
397:Higgs mechanism
377:
367:
366:
352:Proca equations
337:
329:
328:
314:Renormalization
279:Feynman diagram
234:
226:
225:
166:
156:
155:
106:
91:
89:Feynman diagram
43:
28:
23:
22:
15:
12:
11:
5:
3961:
3951:
3950:
3948:Quantum states
3945:
3940:
3923:
3922:
3920:
3919:
3908:
3905:
3904:
3902:
3901:
3896:
3891:
3886:
3885:
3884:
3873:
3871:
3867:
3866:
3864:
3863:
3858:
3853:
3852:
3851:
3841:
3836:
3834:Casimir effect
3831:
3825:
3823:
3819:
3818:
3816:
3815:
3810:
3805:
3800:
3795:
3793:Quantum optics
3790:
3785:
3780:
3775:
3770:
3765:
3760:
3755:
3750:
3745:
3740:
3735:
3730:
3725:
3720:
3715:
3714:
3713:
3703:
3698:
3693:
3688:
3687:
3686:
3676:
3671:
3666:
3660:
3658:
3652:
3651:
3649:
3648:
3643:
3638:
3633:
3628:
3623:
3618:
3613:
3608:
3603:
3598:
3592:
3590:
3584:
3583:
3581:
3580:
3575:
3570:
3568:Quantum eraser
3565:
3560:
3555:
3550:
3545:
3540:
3535:
3530:
3524:
3522:
3518:
3517:
3515:
3514:
3509:
3504:
3499:
3494:
3489:
3484:
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3482:
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3455:
3450:
3445:
3439:
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3430:
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3427:
3422:
3417:
3412:
3407:
3401:
3399:
3395:
3394:
3392:
3391:
3386:
3381:
3376:
3371:
3366:
3361:
3355:
3353:
3349:
3348:
3346:
3345:
3344:
3343:
3338:
3328:
3323:
3318:
3313:
3308:
3303:
3298:
3293:
3288:
3283:
3278:
3273:
3268:
3267:
3266:
3261:
3256:
3251:
3241:
3239:Density matrix
3236:
3231:
3226:
3220:
3218:
3214:
3213:
3211:
3210:
3205:
3200:
3195:
3194:
3193:
3183:
3177:
3175:
3171:
3170:
3163:
3162:
3155:
3148:
3140:
3134:
3133:
3126:
3125:External links
3123:
3122:
3121:
3114:
3099:
3093:
3086:
3065:
3062:
3059:
3058:
3038:
3017:
2982:
2961:
2940:
2938:, pp. 287â288.
2919:
2898:
2890:Thermodynamics
2881:
2864:
2844:
2829:
2778:
2771:
2739:
2732:
2709:
2702:
2677:
2659:
2634:
2627:
2600:
2590:
2570:
2563:
2543:
2529:
2506:
2484:
2446:hep-ph/0607118
2439:(14): 140402.
2423:
2400:
2369:
2320:
2314:hep-th/0610088
2299:
2246:
2229:
2222:
2198:
2177:
2150:
2143:
2120:
2108:
2083:
2076:
2056:
2049:
2022:
2021:
2019:
2016:
2014:
2013:
2011:Casimir effect
2008:
2002:
1997:
1992:
1987:
1982:
1977:
1972:
1966:
1964:
1961:
1948:
1945:
1941:
1937:
1933:
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1926:
1906:
1878:
1874:
1853:
1850:
1846:
1833:
1830:
1756:
1753:
1675:
1669:
1666:
1661:
1658:
1655:
1652:
1649:
1610:Main article:
1607:
1604:
1577:
1573:
1569:
1566:
1542:
1535:
1520:
1500:
1492:Main article:
1489:
1486:
1482:standard model
1437:
1434:
1414:Casimir effect
1402:Main article:
1399:
1396:
1384:Standard Model
1360:field operator
1305:Main article:
1302:
1299:
1267:Standard Model
1193:quantum vacuum
1179:
1178:
1176:
1175:
1168:
1161:
1153:
1150:
1149:
1142:
1141:
1136:
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403:
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399:
394:
389:
384:
378:
375:Standard Model
373:
372:
369:
368:
365:
364:
359:
354:
349:
344:
342:Dirac equation
338:
335:
334:
331:
330:
327:
326:
324:Wick's theorem
321:
316:
311:
309:Regularization
306:
301:
296:
291:
286:
281:
276:
271:
266:
261:
256:
251:
246:
241:
235:
232:
231:
228:
227:
224:
223:
218:
216:Noether charge
213:
208:
203:
201:Gauge symmetry
198:
193:
188:
183:
178:
173:
167:
162:
161:
158:
157:
154:
153:
148:
143:
138:
133:
128:
123:
118:
113:
107:
104:
103:
100:
99:
93:
92:
87:
79:
78:
62:excited states
26:
9:
6:
4:
3:
2:
3960:
3949:
3946:
3944:
3941:
3939:
3936:
3935:
3933:
3918:
3910:
3909:
3906:
3900:
3897:
3895:
3892:
3890:
3887:
3883:
3880:
3879:
3878:
3875:
3874:
3872:
3868:
3862:
3859:
3857:
3854:
3850:
3847:
3846:
3845:
3842:
3840:
3837:
3835:
3832:
3830:
3827:
3826:
3824:
3820:
3814:
3811:
3809:
3806:
3804:
3801:
3799:
3796:
3794:
3791:
3789:
3786:
3784:
3781:
3779:
3776:
3774:
3771:
3769:
3766:
3764:
3761:
3759:
3756:
3754:
3753:Quantum logic
3751:
3749:
3746:
3744:
3741:
3739:
3736:
3734:
3731:
3729:
3726:
3724:
3721:
3719:
3716:
3712:
3709:
3708:
3707:
3704:
3702:
3699:
3697:
3694:
3692:
3689:
3685:
3682:
3681:
3680:
3677:
3675:
3672:
3670:
3667:
3665:
3662:
3661:
3659:
3657:
3653:
3647:
3644:
3642:
3639:
3637:
3634:
3632:
3629:
3627:
3624:
3622:
3619:
3617:
3614:
3612:
3609:
3607:
3606:Quantum chaos
3604:
3602:
3599:
3597:
3594:
3593:
3591:
3589:
3585:
3579:
3576:
3574:
3573:SternâGerlach
3571:
3569:
3566:
3564:
3561:
3559:
3556:
3554:
3551:
3549:
3546:
3544:
3541:
3539:
3536:
3534:
3531:
3529:
3526:
3525:
3523:
3519:
3513:
3510:
3508:
3507:Transactional
3505:
3503:
3500:
3498:
3497:Quantum logic
3495:
3493:
3490:
3488:
3485:
3479:
3476:
3475:
3474:
3471:
3470:
3469:
3466:
3464:
3461:
3459:
3456:
3454:
3451:
3449:
3446:
3444:
3441:
3440:
3438:
3436:
3432:
3426:
3423:
3421:
3418:
3416:
3413:
3411:
3408:
3406:
3403:
3402:
3400:
3396:
3390:
3387:
3385:
3382:
3380:
3377:
3375:
3372:
3370:
3367:
3365:
3362:
3360:
3357:
3356:
3354:
3350:
3342:
3339:
3337:
3334:
3333:
3332:
3331:Wave function
3329:
3327:
3324:
3322:
3319:
3317:
3314:
3312:
3309:
3307:
3306:Superposition
3304:
3302:
3301:Quantum state
3299:
3297:
3294:
3292:
3289:
3287:
3284:
3282:
3279:
3277:
3274:
3272:
3269:
3265:
3262:
3260:
3257:
3255:
3254:Excited state
3252:
3250:
3247:
3246:
3245:
3242:
3240:
3237:
3235:
3232:
3230:
3227:
3225:
3222:
3221:
3219:
3215:
3209:
3206:
3204:
3201:
3199:
3196:
3192:
3189:
3188:
3187:
3184:
3182:
3179:
3178:
3176:
3172:
3168:
3161:
3156:
3154:
3149:
3147:
3142:
3141:
3138:
3132:
3129:
3128:
3119:
3115:
3110:
3105:
3100:
3098:
3094:
3091:
3087:
3084:
3083:3-87144-889-3
3080:
3076:
3072:
3068:
3067:
3055:
3052:: 021301(R),
3051:
3048:
3042:
3035:
3034:0-12-498080-5
3031:
3027:
3021:
3013:
3009:
3005:
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2997:
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2986:
2979:
2978:0-12-498080-5
2975:
2971:
2965:
2958:
2957:0-12-498080-5
2954:
2950:
2944:
2937:
2936:0-387-07295-0
2933:
2929:
2923:
2916:
2915:0-88318-797-3
2912:
2908:
2902:
2895:
2891:
2885:
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2874:
2868:
2861:
2857:
2853:
2852:Fowler, Ralph
2848:
2840:
2836:
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2427:
2420:
2416:
2412:
2411:
2404:
2397:
2393:
2389:
2385:
2384:
2383:Nonlinear QED
2380:
2373:
2365:
2361:
2357:
2353:
2349:
2345:
2340:
2335:
2331:
2324:
2315:
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2187:
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2170:
2166:
2162:
2154:
2146:
2140:
2136:
2135:
2127:
2125:
2117:
2112:
2098:on 2008-01-29
2097:
2093:
2087:
2079:
2073:
2069:
2068:
2060:
2052:
2046:
2042:
2041:
2040:
2030:
2028:
2023:
2012:
2009:
2006:
2003:
2001:
1998:
1996:
1993:
1991:
1988:
1986:
1983:
1981:
1978:
1976:
1975:Vacuum energy
1973:
1971:
1968:
1967:
1960:
1943:
1935:
1927:
1904:
1896:
1892:
1848:
1829:
1826:
1818:
1816:
1812:
1805:
1802:
1798:
1794:
1790:
1784:
1780:
1778:
1774:
1770:
1766:
1762:
1759:According to
1752:
1749:
1743:
1738:
1734:and momentum
1732:
1727:
1723:
1719:
1714:
1709:
1705:
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1697:
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1673:
1667:
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1650:
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1631:
1627:
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1603:
1601:
1597:
1596:Kerr constant
1593:
1575:
1571:
1567:
1564:
1556:
1552:
1548:
1547:birefringence
1541:
1534:
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1427:
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1415:
1411:
1405:
1404:Vacuum energy
1395:
1393:
1389:
1385:
1381:
1377:
1373:
1369:
1365:
1361:
1358:(VEV) of any
1357:
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1341:
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1308:
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1241:
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1233:
1229:
1224:
1222:
1218:
1212:
1210:
1206:
1202:
1201:quantum state
1198:
1194:
1190:
1186:
1174:
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1162:
1160:
1155:
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1152:
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1132:
1130:
1127:
1125:
1122:
1120:
1117:
1115:
1114:Zamolodchikov
1112:
1110:
1109:Zamolodchikov
1107:
1105:
1102:
1100:
1097:
1095:
1092:
1090:
1087:
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1080:
1077:
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1007:
1005:
1002:
1000:
997:
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992:
990:
987:
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832:
830:
827:
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822:
820:
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815:
812:
810:
807:
805:
802:
800:
797:
795:
792:
790:
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785:
782:
780:
777:
775:
772:
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767:
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762:
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460:
457:
455:
452:
451:
444:
443:
436:
433:
431:
428:
426:
423:
421:
420:Supersymmetry
418:
416:
415:String theory
413:
412:
406:
405:
398:
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393:
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388:
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127:
124:
122:
119:
117:
114:
112:
109:
108:
102:
101:
98:
95:
94:
90:
85:
81:
80:
77:
74:
73:
67:
63:
59:
55:
51:
50:Energy levels
47:
41:
37:
33:
19:
3636:Quantum mind
3548:FranckâHertz
3410:KleinâGordon
3359:Formulations
3352:Formulations
3281:Interference
3271:Entanglement
3249:Ground state
3244:Energy level
3217:Fundamentals
3181:Introduction
3096:
3089:
3049:
3046:
3041:
3025:
3020:
2995:
2991:
2985:
2969:
2964:
2948:
2943:
2927:
2922:
2906:
2901:
2893:
2889:
2884:
2876:
2875:, volume 1,
2872:
2867:
2859:
2847:
2794:
2762:
2753:
2742:
2723:
2712:
2693:
2688:
2680:
2670:
2666:
2664:
2650:
2645:
2637:
2612:
2603:
2595:
2580:
2573:
2553:
2546:
2534:
2519:
2509:
2487:
2436:
2432:
2426:
2418:
2414:
2409:
2403:
2391:
2387:
2382:
2378:
2372:
2329:
2323:
2302:
2262:(12): 2654.
2259:
2255:
2249:
2232:
2213:
2208:
2201:
2190:. Retrieved
2168:
2164:
2153:
2133:
2111:
2100:. Retrieved
2096:the original
2086:
2066:
2059:
2038:
2036:
1835:
1824:
1820:
1807:
1786:
1782:
1764:
1758:
1747:
1736:
1730:
1725:
1721:
1712:
1707:
1703:
1691:
1687:
1615:
1539:
1532:
1517:nonlinearity
1497:
1442:relativistic
1439:
1407:
1348:ground state
1340:ground state
1333:
1264:
1225:
1213:
1208:
1197:vacuum state
1196:
1192:
1188:
1182:
1143:
989:Stueckelberg
729:Jona-Lasinio
319:Vacuum state
304:Quantization
146:Gauge theory
126:Strong force
111:Field theory
18:Vacuum state
3894:EPR paradox
3674:Quantum bus
3543:Double-slit
3521:Experiments
3487:Many-worlds
3425:Schrödinger
3389:Phase space
3379:Schrödinger
3369:Interaction
3326:Uncertainty
3296:Nonlocality
3291:Measurement
3286:Decoherence
3276:Hamiltonian
2998:(1): 1â23.
1551:Kerr effect
1529:anisotropic
1527:, becoming
1388:Higgs field
1380:condensates
1129:Zinn-Justin
979:Sommerfield
904:Pomeranchuk
874:Osterwalder
869:Oppenheimer
799:ĆopuszaĆski
624:Fredenhagen
425:Technicolor
3932:Categories
3822:Extensions
3656:Technology
3502:Relational
3453:Copenhagen
3364:Heisenberg
3311:Tunnelling
3174:Background
2791:Paul Busch
2748:Paul Busch
2339:1803.07547
2192:2012-02-06
2102:2008-02-29
2018:References
1980:Lamb shift
1893:(see also
1811:Lamb shift
1773:Guggenheim
1746:= i
1694:being the
1513:QED vacuum
1470:Lagrangian
1368:BCS theory
1283:QCD vacuum
1228:QED vacuum
1124:Zimmermann
1019:Vainshtein
764:Kontsevich
709:Iliopoulos
684:Heisenberg
509:Bogoliubov
447:Scientists
299:Propagator
186:T-symmetry
181:P-symmetry
176:C-symmetry
164:Symmetries
121:Weak force
105:Background
3528:Bell test
3398:Equations
3224:Born rule
3095:H. Genz,
3036:, p. 418.
2980:, p. 239.
2917:, p. 342.
2537:variances
2500:0704.0748
2269:1209.0209
1947:⟩
1936:ϕ
1925:⟨
1905:ϕ
1877:⟩
1852:⟩
1832:Notations
1744:(such as
1665:ℏ
1660:≥
1654:Δ
1648:Δ
1630:variances
1600:dichroism
1568:×
1382:. In the
1248:Schwinger
1221:particles
1199:) is the
1059:Wetterich
1044:Weisskopf
994:Sudarshan
944:Schwinger
859:Nishijima
824:Maldacena
789:Leutwyler
754:Kinoshita
654:Goldstone
644:Gell-Mann
559:Doplicher
336:Equations
3917:Category
3711:Timeline
3463:Ensemble
3443:Bayesian
3336:Collapse
3208:Glossary
3191:Timeline
2959:, p. xv.
2858:(1965).
2839:14119708
2479:43654455
2471:17155223
2396:pdf file
2294:39308527
1963:See also
1436:Symmetry
1289:and the
1254:and the
1244:Tomonaga
1074:Wightman
1039:Weinberg
1029:Virasoro
1009:Tomonaga
1004:Thirring
999:Symanzik
959:Semenoff
934:Schrader
899:Polyakov
819:Majorana
759:Klebanov
714:Ivanenko
704:'t Hooft
674:Guralnik
619:Fröhlich
614:Fritzsch
609:Frampton
524:Buchholz
469:Bargmann
459:Anderson
259:Crossing
54:electron
3870:Related
3849:History
3588:Science
3420:Rydberg
3186:History
3000:Bibcode
2809:Bibcode
2451:Bibcode
2381:; § XI
2364:4931745
2344:Bibcode
2274:Bibcode
1793:Milonni
1716:is the
1686:(with Î
1626:average
1620:of the
1468:of the
1378:called
1366:or the
1240:Feynman
1084:Wilczek
1049:Wentzel
1024:Veltman
969:Shirkov
964:Shifman
954:Seiberg
939:Schwarz
919:Rubakov
844:Naimark
794:Lipatov
784:Lehmann
749:Kendall
639:Gelfand
634:Glashow
594:Feynman
574:Faddeev
569:Englert
539:Coleman
529:Cachazo
514:Brodsky
499:Bjorken
489:Berezin
479:Belavin
239:Anomaly
97:History
52:for an
3943:Vacuum
3563:Popper
3081:
3032:
2976:
2955:
2934:
2913:
2837:
2827:
2769:
2730:
2700:
2657:
2625:
2588:
2561:
2527:
2477:
2469:
2362:
2292:
2242:C-SPAN
2220:
2175:
2141:
2074:
2047:
1889:. The
1771:&
1769:Fowler
1696:energy
1460:. The
1454:scalar
1440:For a
1398:Energy
1281:, and
1246:, and
1205:energy
1187:, the
1139:Zumino
1104:Yukawa
1094:Witten
1089:Wilson
1079:Wigner
1014:Tyutin
974:Skyrme
924:Ruelle
894:Plefka
889:Peskin
879:Parisi
839:MĂžller
829:Migdal
814:Maiani
809:LĂŒders
774:Landau
769:Kuraev
744:KÀllén
734:Jordan
719:Jackiw
659:Gribov
549:DeWitt
544:Dashen
534:Callan
504:Bleuer
474:Becchi
464:Anselm
56:in an
36:Vacuum
3473:Local
3415:Pauli
3405:Dirac
3104:arXiv
2835:S2CID
2799:arXiv
2495:arXiv
2475:S2CID
2441:arXiv
2417:vol.
2390:vol.
2360:S2CID
2334:arXiv
2309:arXiv
2290:S2CID
2264:arXiv
1690:and Î
1458:VEV's
1350:of a
1134:Zuber
984:Stora
949:Segal
929:Salam
914:Proca
909:Popov
884:Pauli
864:Oehme
854:Neveu
849:Nambu
834:Mills
724:Jaffe
699:Hagen
694:Higgs
669:Gupta
664:Gross
649:Glimm
629:Furry
599:Fierz
589:Fermi
584:Fayet
579:Fadin
564:Dyson
554:Dirac
519:Brout
494:Bethe
454:Adler
233:Tools
64:. In
3079:ISBN
3030:ISBN
2974:ISBN
2953:ISBN
2932:ISBN
2911:ISBN
2825:ISBN
2767:ISBN
2728:ISBN
2698:ISBN
2655:ISBN
2623:ISBN
2586:ISBN
2559:ISBN
2525:ISBN
2467:PMID
2218:ISBN
2173:ISBN
2139:ISBN
2072:ISBN
2045:ISBN
1700:time
1698:and
1565:1.32
1265:The
1226:The
1219:and
1099:Yang
1069:Wick
1064:Weyl
1054:Wess
1034:Ward
739:Jost
689:Hepp
679:Haag
604:Fock
484:Bell
58:atom
3073:by
3008:doi
2996:115
2817:doi
2619:106
2459:doi
2419:135
2352:doi
2282:doi
1864:or
1503:of
1462:VEV
1426:erg
1370:of
1230:of
1195:or
1183:In
1119:Zee
804:Low
779:Lee
3934::
3120:".
3050:72
3006:.
2994:.
2854:;
2833:.
2823:.
2815:.
2807:.
2781:^
2765:.
2763:ff
2760:77
2722:.
2696:.
2694:ff
2671:ÎE
2667:Ît
2663:.
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2473:.
2465:.
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2392:78
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2358:.
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2342:.
2288:.
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2163:.
2123:^
2026:^
1959:.
1813:,
1640::
1576:18
1572:10
1484:.
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1330:.
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3159:e
3152:t
3145:v
3112:.
3106::
3092:.
3085:.
3056:.
3014:.
3010::
3002::
2841:.
2819::
2811::
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2775:.
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2673:.
2631:.
2567:.
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2497::
2481:.
2461::
2453::
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2398:.
2366:.
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2346::
2336::
2317:.
2311::
2296:.
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2266::
2226:.
2195:.
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2118:.
2105:.
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2007:*
1944:0
1940:|
1932:|
1928:0
1873:|
1849:0
1845:|
1825:α
1748:ħ
1737:p
1731:q
1726:E
1722:t
1713:ħ
1708:t
1704:E
1692:t
1688:E
1674:,
1668:2
1657:t
1651:E
1543:0
1540:Ό
1536:0
1533:Ό
1521:0
1501:0
1499:Δ
1172:e
1165:t
1158:v
42:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
