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Virtual particle

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existence and non-existence cease to be coherent with each other and do not interfere any more. In the quantum field theory view, actual particles are viewed as being detectable excitations of underlying quantum fields. Virtual particles are also viewed as excitations of the underlying fields, but appear only as forces, not as detectable particles. They are "temporary" in the sense that they appear in some calculations, but are not detected as single particles. Thus, in mathematical terms, they never appear as indices to the
1755: 584: 507: 2839: 214:; that is, as terms in a perturbative calculation. They also appear as an infinite set of states to be summed or integrated over in the calculation of a semi-non-perturbative effect. In the latter case, it is sometimes said that virtual particles contribute to a mechanism that mediates the effect, or that the effect occurs through the virtual particles. 113:. The accuracy and use of virtual particles in calculations is firmly established, but as they cannot be detected in experiments, deciding how to precisely describe them is a topic of debate. Although widely used, they are by no means a necessary feature of QFT, but rather are mathematical conveniences — as demonstrated by 108:
The term is somewhat loose and vaguely defined, in that it refers to the view that the world is made up of "real particles". "Real particles" are better understood to be excitations of the underlying quantum fields. Virtual particles are also excitations of the underlying fields, but are "temporary"
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The lifetime of real particles is typically vastly longer than the lifetime of the virtual particles. Electromagnetic radiation consists of real photons which may travel light years between the emitter and absorber, but (Coulombic) electrostatic attraction and repulsion is a relatively short-range
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For the gravitational and electromagnetic forces, the zero rest-mass of the associated boson particle permits long-range forces to be mediated by virtual particles. However, in the case of photons, power and information transfer by virtual particles is a relatively short-range phenomenon (existing
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Written in the usual mathematical notations, in the equations of physics, there is no mark of the distinction between virtual and actual particles. The amplitudes of processes with a virtual particle interfere with the amplitudes of processes without it, whereas for an actual particle the cases of
799:, any object or process that exists for a limited time or in a limited volume cannot have a precisely defined energy or momentum. For this reason, virtual particles – which exist only temporarily as they are exchanged between ordinary particles – do not typically obey the 272:. In symmetric 3-dimensional space, this exchange results in the inverse cube law for magnetic force. Since the photon has no mass, the magnetic potential has an infinite range. Even though the range is infinite, the time lapse allowed for a virtual photon existence is not infinite. 423:
of radio antennas, where the magnetic and electric effects of the changing current in the antenna wire and the charge effects of the wire's capacitive charge may be (and usually are) important contributors to the total EM field close to the source, but both of which effects are
448:. As distance from the antenna grows, the near-field effects (as dipole fields) die out more quickly, and only the "radiative" effects that are due to actual photons remain as important effects. Although virtual effects extend to infinity, they drop off in field strength as 706:. Here, the explanation of the effect requires that the total energy of all of the virtual particles in a vacuum can be added together. Thus, although the virtual particles themselves are not directly observable in the laboratory, they do leave an observable effect: Their 198:
may be considered a manifestation of virtual particle exchanges. The range of forces carried by virtual particles is limited by the uncertainty principle, which regards energy and time as conjugate variables; thus, virtual particles of larger mass have more limited range.
526:. The appeal of the Feynman diagrams is strong, as it allows for a simple visual presentation of what would otherwise be a rather arcane and abstract formula. In particular, part of the appeal is that the outgoing legs of a Feynman diagram can be associated with actual, 740:
which can be of any kind. These pairs exist for an extremely short time, and then mutually annihilate, or in some cases, the pair may be boosted apart using external energy so that they avoid annihilation and become actual particles, as described below.
440:, are composed of actual photons. Actual and virtual photons are mixed near an antenna, with the virtual photons responsible only for the "extra" magnetic-inductive and transient electric-dipole effects, which cause any imbalance between 133:, an approximation scheme in which interactions (in essence, forces) between actual particles are calculated in terms of exchanges of virtual particles. Such calculations are often performed using schematic representations known as 234:
only within a few wavelengths of the field-disturbance, which carries information or transferred power), as for example seen in the characteristically short range of inductive and capacitative effects in the
66:(QFT) where interactions between ordinary particles are described in terms of exchanges of virtual particles. A process involving virtual particles can be described by a schematic representation known as a 192:
over longer distances and times. As a consequence, a real photon is massless and thus has only two polarization states, whereas a virtual one, being effectively massive, has three polarization states.
85:. The closer its characteristics come to those of ordinary particles, the longer the virtual particle exists. They are important in the physics of many processes, including particle scattering and 323:
during the decay of an excited atom or excited nucleus; such a decay is prohibited by ordinary quantum mechanics and requires the quantization of the electromagnetic field for its explanation.
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requires the use of some rather large and complicated integrals over a large number of variables. These integrals do, however, have a regular structure, and may be represented as
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particles. Thus, it is natural to associate the other lines in the diagram with particles as well, called the "virtual particles". In mathematical terms, they correspond to the
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when they are free and actual, virtual interactions are characterized by the relatively short range of the force interaction produced by particle exchange.
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can lead to a short range, too. Examples of such short-range interactions are the strong and weak forces, and their associated field bosons.
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is not conserved. Examples of macroscopic virtual phonons, photons, and electrons in the case of the tunneling process were presented by
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There are many observable physical phenomena that arise in interactions involving virtual particles. For bosonic particles that exhibit
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There are two principal ways in which the notion of virtual particles appears in modern physics. They appear as intermediate terms in
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for the system. This implies the number of particles in an area of space is not a well-defined quantity but, like other quantum
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are merged to very briefly form a nucleus with a charge greater than about 140, (that is, larger than about the inverse of the
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effects that decay with increasing distance from the antenna much more quickly than do the influence of "conventional"
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is given by the difference between the four-momenta of the particles entering and leaving the interaction vertex,
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in the sense that they appear in calculations of interactions, but never as asymptotic states or indices to the
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of the quantized electromagnetic field causes attraction between a pair of electrically neutral metal plates.
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that exhibits some of the characteristics of an ordinary particle, while having its existence limited by the
2789: 2424: 1785: 1539: 847: 772: 382: 369: 365: 803:; the longer a virtual particle exists, the more the energy and momentum approach the mass-shell relation. 2724: 2061: 1716: 800: 776: 184: 1353: 2811: 1478: 796: 696: 652: 491: 487: 429: 55: 278:. This phenomenon transfers energy to and from a magnetic coil via a changing (electro)magnetic field. 1726: 1442: 1291: 1248: 1138: 1032: 950: 842: 515: 316: 282: 130: 114: 63: 2826: 1809: 1670: 748:, the virtual particles may appear to be actual to the accelerating observer; this is known as the 733: 616: 467: 352: 344: 338: 2838: 2769: 1778: 1736: 1711: 1458: 1432: 1371: 1307: 1264: 1238: 1160: 940: 914: 857: 752:. In short, the vacuum of a stationary frame appears, to the accelerated observer, to be a warm 745: 474:, the roles of electrons, positrons and photons in field theory are replaced by electrons in the 420: 355:, which is the spontaneous production of particle-antiparticle pairs (such as electron-positron). 305: 254: 235: 195: 1635: 257:
for electric force. Since the photon has no mass, the coulomb potential has an infinite range.
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or attraction between two charges—can be thought of as resulting from the exchange of
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Another example is pair production in very strong electric fields, sometimes called
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In the adjacent image, the solid lines correspond to actual particles (of momentum p
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Lambrecht, Astrid (September 2002). "The Casimir effect: a force from nothing".
1303: 607:. The solid lines correspond to a fermion propagator, the wavy lines to bosons. 506: 1496: 1454: 702:
An important example of the "presence" of virtual particles in a vacuum is the
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and so on), while the dotted line corresponds to a virtual particle carrying
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Some field interactions which may be seen in terms of virtual particles are:
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rather than the field of EM waves composed of actual photons, which drop as
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A radically modern approach to introductory physics: volume 2: four forces
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Stahlhofen, A.; Nimtz, G. (2006). "Evanescent modes are virtual photons".
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Are virtual particles really constantly popping in and out of existence?
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Jaffe, R. L. (12 July 2005). "Casimir effect and the quantum vacuum".
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Virtual particles are often popularly described as coming in pairs, a
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as the corresponding ordinary particle, although they always conserve
2663: 2658: 2287: 2274: 2265: 2087: 2001: 1900: 1599: 881:"Far" in terms of ratio of antenna length or diameter, to wavelength. 557: 483: 425: 320: 269: 265: 250: 78: 714:. On the other hand, the Casimir effect can be interpreted as the 2688: 2628: 2480: 2339: 2218: 2158: 2113: 2006: 1984: 1827: 1243: 683:. Since these particles are not certain to exist, they are called 592: 582: 577: 569: 505: 290: 286: 150:
both momentum and energy are conserved at the interaction vertices
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force that is a consequence of the exchange of virtual photons .
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or vibrations of the crystal lattice. A virtual particle is in a
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that are "far" from the source. These far-field waves, for which
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Nimtz, G. (2009). "On virtual phonons, photons, and electrons".
565: 556:, the dotted line would correspond to the exchange of a virtual 253:. In symmetric 3-dimensional space this exchange results in the 74: 70:, in which virtual particles are represented by internal lines. 1774: 1512: 1206:"Ephemeral vacuum particles induce speed-of-light fluctuations" 890:
The electrical power in the fields, respectively, decrease as
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results in forces acting on suitably arranged metal plates or
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for practical communications applications of near fields.
1331:. Socorro, NM: New Mexico Tech Press. pp. 252–254. 1137:(Reprint. ed.). Cambridge : Cambridge Univ. Press. 667:). In many cases, the particle number operator does not 548:. For example, if the solid lines were to correspond to 1182:
Superstrings and other things : a guide to physics
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This may occur in one of two ways. In an accelerating
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Virtual particles do not necessarily carry the same
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Cambridge: Cambridge University Press. 1078: 1076: 1074: 1054: 1044: 587:One-loop diagram with fermion propagator 510:One particle exchange scattering diagram 466:Most of these have analogous effects in 289:is the result of interaction of virtual 975:An Introduction to Quantum Field Theory 932: 874: 795:As a consequence of quantum mechanical 27:Transient quantum fluctuation (physics) 1158: 973:Peskin, M.E., Schroeder, D.V. (1995). 368:, which defines the ratio between the 1354:"A vacuum can yield flashes of light" 1352:Choi, Charles Q. (13 February 2013). 576:, the dotted line would be a virtual 564:, the dotted line would be a virtual 308:is the result of exchange by virtual 7: 946:Introduction to Elementary Particles 917:for a more detailed discussion. See 1133:Walters, Tony Hey; Patrick (2004). 1018:"Are virtual particles less real?" 25: 1759:Template:Quantum mechanics topics 1492:Virtual Particles: What are they? 994:Mandl, F., Shaw, G. (1984/2002). 697:time-energy uncertainty principle 2837: 2730:Timeline of particle discoveries 1754: 1753: 1631:Anomalous magnetic dipole moment 716:relativistic van der Waals force 663:(sometimes collectively called 39:Quantum vacuum (disambiguation) 560:. In the case of interacting 361:of positions of atomic levels. 1: 818:Anomalous photovoltaic effect 767:. If, for example, a pair of 2746:History of subatomic physics 791:Compared to actual particles 572:interacting by means of the 552:interacting by means of the 238:zone of coils and antennas. 1554:Euler–Heisenberg Lagrangian 554:electromagnetic interaction 103:electromagnetic interaction 50:is a theoretical transient 2885: 1455:10.1103/PhysRevD.72.021301 1325:Raymond, David J. (2012). 725: 614: 534:appearing in the diagram. 498:and Alfons A. Stahlhofen. 37:For related articles, see 36: 29: 2835: 2520: 1745: 1569:Path integral formulation 1410:10.1088/2058-7058/15/9/29 1367:10.1038/nature.2013.12430 1304:10.1209/epl/i2006-10271-9 1261:10.1007/s10701-009-9356-z 1180:Calle, Carlos I. (2010). 1108:Hawking, Stephen (1998). 758:thermodynamic equilibrium 591:Virtual particles may be 276:Electromagnetic induction 91:electromagnetic repulsion 2763:mathematical formulation 2358:Eta and eta prime mesons 1737:Photon-photon scattering 1135:The new quantum universe 919:near-field communication 681:probability distribution 639:particle number operator 190:destructive interference 157:energy–momentum relation 152:of the Feynman diagram. 30:Not to be confused with 2425:Double-charm tetraquark 1681:Ward–Takahashi identity 1564:Gupta–Bleuler formalism 1540:Quantum electrodynamics 1504:p. 156 popular article 1110:A brief history of time 1085:Modern particle physics 848:Vacuum Rabi oscillation 773:fine-structure constant 756:of actual particles in 383:magnetic field strength 370:electric field strength 366:impedance of free space 1083:Thomson, Mark (2013). 1016:Jaeger, Gregg (2019). 777:dimensionless quantity 679:, is represented by a 588: 511: 419:Much of the so-called 2822:Wave–particle duality 2812:Relativistic particle 1949:Electron antineutrino 1702:Breit–Wheeler process 1641:Klein–Nishina formula 951:John Wiley & Sons 653:annihilation operator 586: 516:scattering amplitudes 509: 492:probability amplitude 430:electromagnetic waves 56:uncertainty principle 2869:Quantum field theory 2052:Faddeev–Popov ghosts 1802:Particles in physics 996:Quantum Field Theory 843:Zero-energy universe 317:spontaneous emission 283:strong nuclear force 131:quantum field theory 115:lattice field theory 64:quantum field theory 2864:Concepts in physics 2827:Particle chauvinism 2770:Subatomic particles 1717:DelbrĂźck scattering 1671:Vacuum polarization 1595:Faddeev–Popov ghost 1486:Scientific American 1447:2005PhRvD..72b1301J 1296:2006EL.....76..189S 1253:2009FoPh...39.1346N 1143:2003nqu..book.....H 1037:2019Entrp..21..141J 801:mass-shell relation 689:vacuum fluctuations 617:Quantum fluctuation 514:The calculation of 468:solid-state physics 353:decay of the vacuum 345:Vacuum polarization 339:van der Waals force 127:perturbation theory 60:perturbation theory 1712:Compton scattering 1499:American Scientist 977:, Westview Press, 915:near and far field 858:Virtual black hole 746:frame of reference 589: 512: 306:weak nuclear force 255:inverse square law 196:Quantum tunnelling 99:exchange particles 2851: 2850: 2807:Massless particle 2615: 2614: 2611: 2610: 2576: 2575: 2439: 2438: 2251: 2250: 2247: 2246: 2199:Magnetic monopole 2147: 2146: 2038: 2037: 1979: 1978: 1959:Muon antineutrino 1944:Electron neutrino 1768: 1767: 1727:Møller scattering 1697:Bhabha scattering 1666:Uehling potential 1615:Virtual particles 1425:Physical Review D 1338:978-0-98303-946-4 1237:(12): 1346–1355. 1046:10.3390/e21020141 960:978-3-527-40601-2 708:zero-point energy 685:virtual particles 661:creation operator 568:. In the case of 347:, which involves 264:between magnetic 205:scattering matrix 111:scattering matrix 16:(Redirected from 2876: 2841: 2817:Virtual particle 2588:Mesonic molecule 2522: 2518: 2363:Bottom eta meson 2271: 2262: 2234:W′ and Z′ bosons 2224:Sterile neutrino 2209:Majorana fermion 2076: 2067: 1990: 1969:Tau antineutrino 1824: 1815: 1795: 1788: 1781: 1772: 1757: 1756: 1732:Schwinger effect 1533: 1526: 1519: 1510: 1497:D Kaiser (2005) 1483: 1467: 1466: 1440: 1420: 1414: 1413: 1393: 1387: 1386: 1384: 1382: 1369: 1349: 1343: 1342: 1322: 1316: 1315: 1279: 1273: 1272: 1246: 1226: 1220: 1219: 1217: 1216: 1202: 1196: 1195: 1177: 1171: 1170: 1164: 1156: 1130: 1124: 1123: 1105: 1099: 1098: 1080: 1069: 1068: 1058: 1048: 1022: 1013: 1007: 992: 986: 971: 965: 964: 949:(2nd ed.). 937: 922: 911: 905: 903: 896: 888: 882: 879: 785:Julian Schwinger 665:ladder operators 651:is the particle 605:one-loop diagram 524:Feynman diagrams 520:particle physics 502:Feynman diagrams 461: 454: 447: 443: 439: 435: 415: 413: 407: 393: 391: 380: 378: 212:Feynman diagrams 177: 147: 143: 135:Feynman diagrams 48:virtual particle 21: 2884: 2883: 2879: 2878: 2877: 2875: 2874: 2873: 2854: 2853: 2852: 2847: 2831: 2785:Nuclear physics 2734: 2698: 2634:Davydov soliton 2607: 2572: 2546: 2507: 2435: 2407: 2334: 2243: 2143: 2102: 2056: 2034: 2016: 1975: 1895: 1804: 1799: 1769: 1764: 1763: 1741: 1685: 1676:Vertex function 1661:Schwinger limit 1636:Furry's theorem 1619: 1573: 1559:Feynman diagram 1542: 1537: 1481: 1475: 1470: 1422: 1421: 1417: 1395: 1394: 1390: 1380: 1378: 1351: 1350: 1346: 1339: 1324: 1323: 1319: 1281: 1280: 1276: 1228: 1227: 1223: 1214: 1212: 1204: 1203: 1199: 1192: 1179: 1178: 1174: 1157: 1153: 1132: 1131: 1127: 1120: 1107: 1106: 1102: 1095: 1082: 1081: 1072: 1020: 1015: 1014: 1010: 993: 989: 972: 968: 961: 941:Griffiths, D.J. 939: 938: 934: 930: 925: 912: 908: 898: 891: 889: 885: 880: 876: 872: 867: 813: 793: 730: 728:Pair production 724: 722:Pair production 631: 615:Main articles: 613: 540: 518:in theoretical 504: 478:, holes in the 476:conduction band 456: 449: 445: 441: 437: 433: 409: 408:| / | 403: 401: 395: 387: 385: 374: 372: 349:pair production 220: 159: 145: 141: 123: 95:virtual photons 68:Feynman diagram 42: 35: 28: 23: 22: 18:Virtual photons 15: 12: 11: 5: 2882: 2880: 2872: 2871: 2866: 2856: 2855: 2849: 2848: 2844:Physics portal 2836: 2833: 2832: 2830: 2829: 2824: 2819: 2814: 2809: 2804: 2799: 2798: 2797: 2787: 2782: 2777: 2772: 2767: 2766: 2765: 2758:Standard Model 2755: 2754: 2753: 2742: 2740: 2736: 2735: 2733: 2732: 2727: 2725:Quasiparticles 2722: 2717: 2712: 2706: 2704: 2700: 2699: 2697: 2696: 2691: 2686: 2681: 2676: 2671: 2666: 2661: 2656: 2651: 2646: 2641: 2636: 2631: 2625: 2623: 2621:Quasiparticles 2617: 2616: 2613: 2612: 2609: 2608: 2606: 2605: 2600: 2595: 2590: 2584: 2582: 2578: 2577: 2574: 2573: 2571: 2570: 2565: 2560: 2554: 2552: 2548: 2547: 2545: 2544: 2539: 2534: 2528: 2526: 2515: 2509: 2508: 2506: 2505: 2500: 2495: 2494: 2493: 2488: 2483: 2478: 2473: 2468: 2458: 2453: 2447: 2445: 2441: 2440: 2437: 2436: 2434: 2433: 2428: 2417: 2415: 2413:Exotic hadrons 2409: 2408: 2406: 2405: 2400: 2395: 2390: 2385: 2380: 2375: 2370: 2365: 2360: 2355: 2350: 2344: 2342: 2336: 2335: 2333: 2332: 2327: 2322: 2317: 2312: 2307: 2306: 2305: 2300: 2295: 2290: 2279: 2277: 2268: 2259: 2253: 2252: 2249: 2248: 2245: 2244: 2242: 2241: 2239:X and Y bosons 2236: 2231: 2226: 2221: 2216: 2211: 2206: 2201: 2196: 2191: 2186: 2181: 2176: 2171: 2166: 2161: 2155: 2153: 2149: 2148: 2145: 2144: 2142: 2141: 2131: 2126: 2121: 2116: 2110: 2108: 2104: 2103: 2101: 2100: 2095: 2090: 2084: 2082: 2073: 2064: 2058: 2057: 2055: 2054: 2048: 2046: 2040: 2039: 2036: 2035: 2033: 2032: 2026: 2024: 2018: 2017: 2015: 2014: 2012:W and Z bosons 2009: 2004: 1998: 1996: 1987: 1981: 1980: 1977: 1976: 1974: 1973: 1972: 1971: 1966: 1961: 1956: 1951: 1946: 1936: 1931: 1926: 1921: 1916: 1911: 1905: 1903: 1897: 1896: 1894: 1893: 1888: 1883: 1878: 1873: 1868: 1866:Strange (quark 1863: 1858: 1853: 1848: 1843: 1838: 1832: 1830: 1821: 1812: 1806: 1805: 1800: 1798: 1797: 1790: 1783: 1775: 1766: 1765: 1762: 1761: 1747: 1746: 1743: 1742: 1740: 1739: 1734: 1729: 1724: 1719: 1714: 1709: 1707:Bremsstrahlung 1704: 1699: 1693: 1691: 1687: 1686: 1684: 1683: 1678: 1673: 1668: 1663: 1658: 1653: 1648: 1643: 1638: 1633: 1627: 1625: 1621: 1620: 1618: 1617: 1612: 1607: 1602: 1597: 1592: 1587: 1581: 1579: 1575: 1574: 1572: 1571: 1566: 1561: 1556: 1550: 1548: 1544: 1543: 1538: 1536: 1535: 1528: 1521: 1513: 1507: 1506: 1494: 1489: 1474: 1473:External links 1471: 1469: 1468: 1438:hep-th/0503158 1415: 1388: 1344: 1337: 1317: 1284:Europhys. Lett 1274: 1221: 1197: 1190: 1172: 1151: 1125: 1118: 1100: 1094:978-1107034266 1093: 1070: 1008: 1006:, pp. 56, 176. 987: 966: 959: 953:. p. 65. 931: 929: 926: 924: 923: 906: 883: 873: 871: 868: 866: 865: 860: 855: 850: 845: 840: 835: 830: 825: 820: 814: 812: 809: 792: 789: 726:Main article: 723: 720: 704:Casimir effect 612: 609: 538: 503: 500: 472:semiconductors 464: 463: 417: 399: 362: 356: 342: 335: 328:Casimir effect 324: 313: 310:W and Z bosons 302: 279: 273: 262:magnetic field 258: 219: 218:Manifestations 216: 185:off mass shell 122: 119: 87:Casimir forces 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 2881: 2870: 2867: 2865: 2862: 2861: 2859: 2846: 2845: 2840: 2834: 2828: 2825: 2823: 2820: 2818: 2815: 2813: 2810: 2808: 2805: 2803: 2802:Exotic matter 2800: 2796: 2793: 2792: 2791: 2790:Eightfold way 2788: 2786: 2783: 2781: 2780:Antiparticles 2778: 2776: 2773: 2771: 2768: 2764: 2761: 2760: 2759: 2756: 2752: 2749: 2748: 2747: 2744: 2743: 2741: 2737: 2731: 2728: 2726: 2723: 2721: 2718: 2716: 2713: 2711: 2708: 2707: 2705: 2701: 2695: 2692: 2690: 2687: 2685: 2682: 2680: 2677: 2675: 2672: 2670: 2667: 2665: 2662: 2660: 2657: 2655: 2652: 2650: 2647: 2645: 2642: 2640: 2637: 2635: 2632: 2630: 2627: 2626: 2624: 2622: 2618: 2604: 2601: 2599: 2596: 2594: 2591: 2589: 2586: 2585: 2583: 2579: 2569: 2566: 2564: 2561: 2559: 2556: 2555: 2553: 2549: 2543: 2540: 2538: 2535: 2533: 2530: 2529: 2527: 2523: 2519: 2516: 2514: 2510: 2504: 2501: 2499: 2496: 2492: 2489: 2487: 2484: 2482: 2479: 2477: 2474: 2472: 2469: 2467: 2464: 2463: 2462: 2459: 2457: 2454: 2452: 2451:Atomic nuclei 2449: 2448: 2446: 2442: 2432: 2429: 2426: 2422: 2419: 2418: 2416: 2414: 2410: 2404: 2401: 2399: 2396: 2394: 2391: 2389: 2386: 2384: 2383:Upsilon meson 2381: 2379: 2376: 2374: 2371: 2369: 2366: 2364: 2361: 2359: 2356: 2354: 2351: 2349: 2346: 2345: 2343: 2341: 2337: 2331: 2328: 2326: 2323: 2321: 2318: 2316: 2315:Lambda baryon 2313: 2311: 2308: 2304: 2301: 2299: 2296: 2294: 2291: 2289: 2286: 2285: 2284: 2281: 2280: 2278: 2276: 2272: 2269: 2267: 2263: 2260: 2258: 2254: 2240: 2237: 2235: 2232: 2230: 2227: 2225: 2222: 2220: 2217: 2215: 2212: 2210: 2207: 2205: 2202: 2200: 2197: 2195: 2192: 2190: 2187: 2185: 2182: 2180: 2177: 2175: 2174:Dual graviton 2172: 2170: 2167: 2165: 2162: 2160: 2157: 2156: 2154: 2150: 2139: 2135: 2132: 2130: 2127: 2125: 2122: 2120: 2117: 2115: 2112: 2111: 2109: 2105: 2099: 2096: 2094: 2091: 2089: 2086: 2085: 2083: 2081: 2077: 2074: 2072: 2071:Superpartners 2068: 2065: 2063: 2059: 2053: 2050: 2049: 2047: 2045: 2041: 2031: 2028: 2027: 2025: 2023: 2019: 2013: 2010: 2008: 2005: 2003: 2000: 1999: 1997: 1995: 1991: 1988: 1986: 1982: 1970: 1967: 1965: 1962: 1960: 1957: 1955: 1954:Muon neutrino 1952: 1950: 1947: 1945: 1942: 1941: 1940: 1937: 1935: 1932: 1930: 1927: 1925: 1922: 1920: 1917: 1915: 1912: 1910: 1907: 1906: 1904: 1902: 1898: 1892: 1889: 1887: 1886:Bottom (quark 1884: 1882: 1879: 1877: 1874: 1872: 1869: 1867: 1864: 1862: 1859: 1857: 1854: 1852: 1849: 1847: 1844: 1842: 1839: 1837: 1834: 1833: 1831: 1829: 1825: 1822: 1820: 1816: 1813: 1811: 1807: 1803: 1796: 1791: 1789: 1784: 1782: 1777: 1776: 1773: 1760: 1752: 1749: 1748: 1744: 1738: 1735: 1733: 1730: 1728: 1725: 1723: 1720: 1718: 1715: 1713: 1710: 1708: 1705: 1703: 1700: 1698: 1695: 1694: 1692: 1688: 1682: 1679: 1677: 1674: 1672: 1669: 1667: 1664: 1662: 1659: 1657: 1654: 1652: 1649: 1647: 1644: 1642: 1639: 1637: 1634: 1632: 1629: 1628: 1626: 1622: 1616: 1613: 1611: 1608: 1606: 1603: 1601: 1598: 1596: 1593: 1591: 1588: 1586: 1583: 1582: 1580: 1576: 1570: 1567: 1565: 1562: 1560: 1557: 1555: 1552: 1551: 1549: 1545: 1541: 1534: 1529: 1527: 1522: 1520: 1515: 1514: 1511: 1505: 1503: 1500: 1495: 1493: 1490: 1487: 1480: 1477: 1476: 1472: 1464: 1460: 1456: 1452: 1448: 1444: 1439: 1434: 1431:(2): 021301. 1430: 1426: 1419: 1416: 1411: 1407: 1403: 1399: 1398:Physics World 1392: 1389: 1377: 1373: 1368: 1363: 1359: 1355: 1348: 1345: 1340: 1334: 1330: 1329: 1321: 1318: 1313: 1309: 1305: 1301: 1297: 1293: 1289: 1285: 1278: 1275: 1270: 1266: 1262: 1258: 1254: 1250: 1245: 1240: 1236: 1232: 1225: 1222: 1211: 1207: 1201: 1198: 1193: 1191:9781439810743 1187: 1183: 1176: 1173: 1168: 1162: 1154: 1152:9780521564571 1148: 1144: 1140: 1136: 1129: 1126: 1121: 1119:9780553896923 1115: 1111: 1104: 1101: 1096: 1090: 1086: 1079: 1077: 1075: 1071: 1066: 1062: 1057: 1052: 1047: 1042: 1038: 1034: 1030: 1026: 1019: 1012: 1009: 1005: 1004:0-471-94186-7 1001: 997: 991: 988: 984: 983:0-201-50397-2 980: 976: 970: 967: 962: 956: 952: 948: 947: 942: 936: 933: 927: 920: 916: 910: 907: 902: 895: 887: 884: 878: 875: 869: 864: 861: 859: 856: 854: 851: 849: 846: 844: 841: 839: 836: 834: 833:Quasiparticle 831: 829: 828:Force carrier 826: 824: 821: 819: 816: 815: 810: 808: 804: 802: 798: 790: 788: 786: 782: 778: 775:, which is a 774: 770: 769:atomic nuclei 766: 761: 759: 755: 751: 747: 742: 739: 735: 729: 721: 719: 717: 713: 709: 705: 700: 699:in a vacuum. 698: 694: 693:vacuum energy 690: 686: 682: 678: 674: 670: 666: 662: 659:the particle 658: 654: 650: 646: 643: 640: 636: 630: 626: 622: 618: 610: 608: 606: 602: 598: 597:vector bosons 594: 585: 581: 580:, and so on. 579: 575: 571: 567: 563: 559: 555: 551: 547: 544: 535: 533: 529: 525: 521: 517: 508: 501: 499: 497: 493: 489: 488:virtual state 485: 481: 477: 473: 469: 460: 453: 431: 427: 422: 418: 412: 406: 398: 390: 384: 377: 371: 367: 363: 360: 357: 354: 350: 346: 343: 340: 336: 333: 329: 325: 322: 318: 314: 311: 307: 303: 300: 296: 292: 288: 284: 280: 277: 274: 271: 267: 263: 259: 256: 252: 248: 247:Coulomb force 244: 243: 242: 239: 237: 231: 229: 225: 217: 215: 213: 208: 206: 200: 197: 193: 191: 187: 186: 181: 176: 173: 169: 165: 162: 158: 153: 151: 140: 139:four-momentum 136: 132: 128: 120: 118: 116: 112: 106: 104: 100: 96: 92: 88: 84: 80: 76: 71: 69: 65: 61: 57: 53: 49: 44: 40: 33: 19: 2842: 2816: 2513:Hypothetical 2461:Exotic atoms 2330:Omega baryon 2320:Sigma baryon 2310:Delta baryon 2062:Hypothetical 2044:Ghost fields 2030:Higgs boson 1964:Tau neutrino 1856:Charm (quark 1750: 1614: 1501: 1498: 1485: 1428: 1424: 1418: 1404:(9): 29–32. 1401: 1397: 1391: 1379:. Retrieved 1357: 1347: 1327: 1320: 1287: 1283: 1277: 1234: 1230: 1224: 1213:. Retrieved 1209: 1200: 1181: 1175: 1134: 1128: 1109: 1103: 1084: 1028: 1024: 1011: 995: 990: 974: 969: 944: 935: 909: 900: 893: 886: 877: 853:Quantum foam 823:False vacuum 805: 794: 765:vacuum decay 762: 750:Unruh effect 743: 738:antiparticle 731: 701: 688: 684: 656: 648: 644: 641: 632: 629:Vacuum state 590: 574:strong force 545: 536: 513: 496:GĂźnter Nimtz 480:valence band 465: 458: 451: 410: 404: 396: 388: 375: 332:ground state 330:, where the 240: 232: 221: 209: 201: 194: 183: 174: 171: 167: 163: 160: 154: 149: 124: 107: 72: 47: 45: 43: 32:Antiparticle 2795:Quark model 2563:Theta meson 2466:Positronium 2378:Omega meson 2373:J/psi meson 2303:Antineutron 2214:Dark photon 2179:Graviphoton 2138:Stop squark 1846:Down (quark 1656:Self-energy 1646:Landau pole 1610:Positronium 1585:Dual photon 1231:Found. Phys 797:uncertainty 712:dielectrics 677:observables 673:Hamiltonian 532:propagators 228:Confinement 2858:Categories 2537:Heptaquark 2498:Superatoms 2431:Pentaquark 2421:Tetraquark 2403:Quarkonium 2293:Antiproton 2194:Leptoquark 2129:Neutralino 1891:antiquark) 1881:antiquark) 1876:Top (quark 1871:antiquark) 1861:antiquark) 1851:antiquark) 1841:antiquark) 1810:Elementary 1722:Lamb shift 1651:QED vacuum 1290:(2): 198. 1215:2017-07-24 1031:(2): 141. 928:References 863:Added mass 635:eigenstate 625:QCD vacuum 621:QED vacuum 490:where the 421:near-field 359:Lamb shift 236:near field 121:Properties 2775:Particles 2720:Particles 2679:Polariton 2669:Plasmaron 2639:Dropleton 2532:Hexaquark 2503:Molecules 2491:Protonium 2368:Phi meson 2353:Rho meson 2325:Xi baryon 2257:Composite 2093:Gravitino 1836:Up (quark 1751:See also: 1690:Processes 1578:Particles 1547:Formalism 1376:124394711 1312:250758644 1269:118594121 1244:0907.1611 1161:cite book 870:Footnotes 787:in 1951. 781:Dirac sea 671:with the 550:electrons 299:rho meson 224:rest mass 2751:timeline 2603:R-hadron 2558:Glueball 2542:Skyrmion 2476:Tauonium 2189:Inflaton 2184:Graviton 2164:Curvaton 2134:Sfermion 2124:Higgsino 2119:Chargino 2080:Gauginos 1939:Neutrino 1924:Antimuon 1914:Positron 1909:Electron 1819:Fermions 1624:Concepts 1605:Positron 1590:Electron 1488:website. 1463:13171179 1381:2 August 1210:Phys.org 1065:33266857 985:, p. 80. 943:(2008). 811:See also 734:particle 647:, where 601:fermions 562:nucleons 543:momentum 528:on-shell 402:= | 381:and the 295:pi meson 285:between 180:velocity 144:, where 101:for the 83:momentum 52:particle 2739:Related 2710:Baryons 2684:Polaron 2674:Plasmon 2649:Fracton 2644:Exciton 2598:Diquark 2593:Pomeron 2568:T meson 2525:Baryons 2486:Pionium 2471:Muonium 2398:D meson 2393:B meson 2298:Neutron 2283:Nucleon 2275:Baryons 2266:Hadrons 2229:Tachyon 2204:Majoron 2169:Dilaton 2098:Photino 1934:Antitau 1901:Leptons 1443:Bibcode 1292:Bibcode 1249:Bibcode 1139:Bibcode 1056:7514619 1033:Bibcode 1025:Entropy 669:commute 637:of the 611:Vacuums 484:phonons 351:or the 270:photons 266:dipoles 251:photons 2715:Mesons 2664:Phonon 2659:Magnon 2581:Others 2551:Mesons 2444:Others 2340:Mesons 2288:Proton 2152:Others 2107:Others 2088:Gluino 2022:Scalar 2002:Photon 1985:Bosons 1828:Quarks 1600:Photon 1482:  1461:  1374:  1358:Nature 1335:  1310:  1267:  1188:  1149:  1116:  1091:  1063:  1053:  1002:  981:  957:  627:, and 593:mesons 570:quarks 558:photon 482:, and 426:dipole 414:| 392:| 386:| 379:| 373:| 321:photon 291:gluons 287:quarks 79:energy 2703:Lists 2694:Trion 2689:Roton 2629:Anyon 2456:Atoms 2219:Preon 2159:Axion 2114:Axino 2007:Gluon 1994:Gauge 1459:S2CID 1433:arXiv 1372:S2CID 1308:S2CID 1265:S2CID 1239:arXiv 1021:(PDF) 736:and 578:gluon 319:of a 2654:Hole 2481:Onia 2388:Kaon 2348:Pion 1919:Muon 1383:2015 1333:ISBN 1186:ISBN 1167:link 1147:ISBN 1114:ISBN 1089:ISBN 1061:PMID 1000:ISBN 979:ISBN 955:ISBN 913:See 897:and 655:and 566:pion 444:and 364:The 337:The 326:The 315:The 304:The 297:and 281:The 260:The 245:The 81:and 75:mass 1929:Tau 1451:doi 1406:doi 1362:doi 1300:doi 1257:doi 1051:PMC 1041:doi 754:gas 691:of 687:or 595:or 129:of 62:of 2860:: 1502:93 1457:. 1449:. 1441:. 1429:72 1427:. 1402:15 1400:. 1370:. 1360:. 1356:. 1306:. 1298:. 1288:76 1286:. 1263:. 1255:. 1247:. 1235:39 1233:. 1208:. 1163:}} 1159:{{ 1145:. 1073:^ 1059:. 1049:. 1039:. 1029:21 1027:. 1023:. 899:1/ 892:1/ 760:. 718:. 623:, 619:, 457:1/ 450:1/ 446:cB 438:cB 394:: 170:− 166:= 105:. 46:A 2427:) 2423:( 2140:) 2136:( 1794:e 1787:t 1780:v 1532:e 1525:t 1518:v 1465:. 1453:: 1445:: 1435:: 1412:. 1408:: 1385:. 1364:: 1341:. 1314:. 1302:: 1294:: 1271:. 1259:: 1251:: 1241:: 1218:. 1194:. 1169:) 1155:. 1141:: 1122:. 1097:. 1067:. 1043:: 1035:: 963:. 904:. 901:r 894:r 657:a 649:a 645:a 642:a 546:k 539:1 462:. 459:r 452:r 442:E 434:E 416:. 411:H 405:E 400:0 397:Z 389:H 376:E 312:. 301:. 175:c 172:p 168:E 164:c 161:m 146:q 142:q 41:. 34:. 20:)

Index

Virtual photons
Antiparticle
Quantum vacuum (disambiguation)
particle
uncertainty principle
perturbation theory
quantum field theory
Feynman diagram
mass
energy
momentum
Casimir forces
electromagnetic repulsion
virtual photons
exchange particles
electromagnetic interaction
scattering matrix
lattice field theory
perturbation theory
quantum field theory
Feynman diagrams
four-momentum
energy–momentum relation
velocity
off mass shell
destructive interference
Quantum tunnelling
scattering matrix
Feynman diagrams
rest mass

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