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Quantum Field Theory and Quantum Electrodynamics

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Part of the Springer Tracts in Modern Physics book series (STMP, volume 274)

Abstract

One of the main reasons why quantities like the anomalous magnetic moment of the muon attract so much attention is their prominent role in basic tests of QFT in general and of Quantum Electrodynamics (QED) and the Standard Model (SM) in particular.

References

  1. 1.
    J.D. Bjorken, S.D. Drell, Relativistic Quantum Mechanics, 1st edn. (McGraw-Hill, New York 1964), 300 p; Relativistic Quantum Fields, 1st edn. (McGraw-Hill, New York, 1965), 396 pGoogle Scholar
  2. 2.
    V.B. Berestetskii, E.M. Lifshitz, L.P. Pitaevskii, Quantum electrodynamics, Landau and Lifshitz Course of Theoretical Physics, vol. 4, 2nd edn. (Pergamon, London, 1982), 652 pGoogle Scholar
  3. 3.
    P.A.M. Dirac, Proc. R. Soc. A 114, 243 (1927); Proc. R. Soc. A 126, 360 (1930); Proc. R. Soc. A 136, 453 (1932)Google Scholar
  4. 4.
    E.P. Wigner, Ann. Math. 40, 149 (1939)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    P. Jordan, E.P. Wigner, Zeits. Phys. 47, 631 (1928)ADSCrossRefGoogle Scholar
  6. 6.
    W. Heisenberg, W. Pauli, Zeits. Phys. 56, 1 (1929); Zeits. Phys. 59, 168 (1930); P.A.M. Dirac, V.A. Fock, B. Podolsky, Phys. Zeits. Sowjetunion 3, 64 (1932)Google Scholar
  7. 7.
    H. Joos, Fortsch. Phys. 10, 65 (1962); S. Weinberg, Phys. Rev. 133, B1318 (1964); Phys. Rev. 134, B882 (1964)Google Scholar
  8. 8.
    P.A.M. Dirac, Proc. R. Soc. A 114, 243 (1927); A 117, 610 (1928)Google Scholar
  9. 9.
    W. Pauli, Zeits. Physik 31, 765 (1925)ADSCrossRefGoogle Scholar
  10. 10.
    W. Pauli, Phys. Rev. 58, 716 (1940)ADSCrossRefGoogle Scholar
  11. 11.
    R.F. Streater, A.S. Wightman, CPT, Spin and Statistics and All That (Benjamin, New York, 1964)Google Scholar
  12. 12.
    G. Lüders, K. Danske Vidensk, Selsk. Mat.-Fys. Medd. 28(5) (1954); W. Pauli, Exclusion principle, Lorentz group and reflection of space-time and charge, in Niels Bohr and the Development of Physics, ed. by W. Pauli (Pergamon Press, London, 1955, reissued 1962), pp. 30–51; W. Pauli, II Nuovo Cim. 6, 204 (1957); G. Lüders, Ann. Phys. N. Y. 2, 1 (1957); G. Lüders, B. Zumino, Phys. Rev. 106, 345 (1957); R. Jost, Helv. Phys. Acta 30, 409 (1957)Google Scholar
  13. 13.
    S. Gasiorovicz, Elementary Particle Physics (Wiley, New York, 1966)Google Scholar
  14. 14.
    S. Eidelman et al. [Particle Data Group], Phys. Lett. B 592, 1 (2004); K.A. Olive et al. [Particle Data Group], Chin. Phys. C 38, 090001 (2014) and 2015 updateGoogle Scholar
  15. 15.
    B.C. Regan, E.D. Commins, C.J. Schmidt, D. DeMille, Phys. Rev. Lett. 88, 071805 (2002)ADSCrossRefGoogle Scholar
  16. 16.
    J. Baron et al. [ACME Collab.], Science 343, 269 (2014)Google Scholar
  17. 17.
    W. Gerlach, O. Stern, Zeits. Physik 8, 110 (1924)ADSCrossRefGoogle Scholar
  18. 18.
    R. Kronig (1925 unpublished), https://en.wikipedia.org/wiki/Ralph_Kronig
  19. 19.
    G.E. Uhlenbeck, S. Goudsmit, Naturwissenschaften 13, 953 (1925); Nature 117, 264 (1926)Google Scholar
  20. 20.
    W. Pauli, Zeits. Phys. 43, 601 (1927)ADSCrossRefGoogle Scholar
  21. 21.
    F. Englert, R. Brout, Phys. Rev. Lett. 13, 321 (1964)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    P.W. Higgs, Phys. Lett. 12, 132 (1964)ADSCrossRefGoogle Scholar
  23. 23.
    G. Aad et al. [ATLAS Collab.], Phys. Lett. B 716, 1 (2012); Science 338, 1576 (2012)Google Scholar
  24. 24.
    S. Chatrchyan et al. [CMS Collab.], Phys. Lett. B 716, 30 (2012); Science 338, 1569 (2012)Google Scholar
  25. 25.
    S. Weinberg, Phys. Rev. 134, B882 (1964)ADSCrossRefGoogle Scholar
  26. 26.
    R. Frisch, O. Stern, Zeits. Physik 85, 4 (1933); I. Estermann, O. Stern, ibid. 85, 17 (1933)Google Scholar
  27. 27.
    G. Charpak, F.J.M. Farley, R.L. Garwin, T. Muller, J.C. Sens, A. Zichichi, Phys. Lett. 1B, 16 (1962)CrossRefGoogle Scholar
  28. 28.
    H. Weyl, Zeits. Phys. 56, 330 (1929)ADSCrossRefGoogle Scholar
  29. 29.
    C.N. Yang, R.L. Mills, Phys. Rev. 96, 191 (1954)ADSCrossRefGoogle Scholar
  30. 30.
    M. Gell-Mann, F. Low, Phys. Rev. 95, 1300 (1954)ADSCrossRefGoogle Scholar
  31. 31.
    G.C. Wick, Phys. Rev. 80, 268 (1950)ADSCrossRefGoogle Scholar
  32. 32.
    W. Pauli, F. Villars, Rev. Mod. Phys. 21, 434 (1949)ADSCrossRefGoogle Scholar
  33. 33.
    N.N. Bogoliubov, D.V. Shirkov, Introduction to the Theory of Quantized Fields, 1st & 2nd edn. (Wiley, New York, 1957, 1980), 720 pGoogle Scholar
  34. 34.
    S. Tomonaga, R. Iho, Progr. Theor. Phys. 1, 27 (1946); J. Schwinger, Phys. Rev. 74, 1439 (1948); R.P. Feynman, Phys. Rev. 76, 749 (1949); F. Dyson, Phys. Rev. 75, 486 (1949), ibid. 1736Google Scholar
  35. 35.
    H. Fritzsch, M. Gell-Mann, H. Leutwyler, Phys. Lett. 47B, 365 (1973)ADSCrossRefGoogle Scholar
  36. 36.
    H.D. Politzer, Phys. Rev. Lett. 30, 1346 (1973); D. Gross, F. Wilczek, Phys. Rev. Lett. 30, 1343 (1973)Google Scholar
  37. 37.
    S.L. Glashow, Nucl. Phys. B 22, 579 (1961); S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967); A. Salam, Weak and electromagnetic interactions, in Elementary Particle Theory, ed. by N. Svartholm (Amquist and Wiksells, Stockholm, 1969), pp. 367–377Google Scholar
  38. 38.
    G. ’t Hooft, Nucl. Phys. B 33, 173 (1971); 35, 167 (1971); G. ’t Hooft, M. Veltman, Nucl. Phys. B 50, 318 (1972)Google Scholar
  39. 39.
    G. t’ Hooft, M. Veltman, Nucl. Phys. B 44, 189 (1972)Google Scholar
  40. 40.
    W.H. Furry, Phys. Rev. 51, 125 (1937)ADSCrossRefGoogle Scholar
  41. 41.
    F. Dyson, Phys. Rev. 75, 1736 (1949); J.S. Schwinger, Proc. Nat. Acad. Sci. 37, 452–459 (1951)Google Scholar
  42. 42.
    H. Lehmann, K. Symanzik, W. Zimmermann, Nuovo Cim. 1, 205 (1955); Nuovo Cim. 6, 319 (1957)Google Scholar
  43. 43.
    S. Mandelstam, Phys. Rev. 112, 1344 (1958)ADSMathSciNetCrossRefGoogle Scholar
  44. 44.
    I. Białynicki-Birula, Phys. Rev. D 2, 2877 (1970)ADSCrossRefGoogle Scholar
  45. 45.
    F. Jegerlehner, Eur. Phys. J. C 18, 673 (2001)ADSCrossRefGoogle Scholar
  46. 46.
    D. Akyeampong, R. Delbourgo, Nuovo Cim. 17A, 47 (1973); W.A. Bardeen, R. Gastmans, B. Lautrup, Nucl. Phys. B 46, 319 (1972); M. Chanowitz, M. Furman, I. Hinchliffe, Nucl. Phys. B 159, 225 (1979)Google Scholar
  47. 47.
    M.C. Bergère, F. David, J. Math. Phys. 20, 1244 (1979)ADSMathSciNetCrossRefGoogle Scholar
  48. 48.
    K. Osterwalder, R. Schrader, Commun. Math. Phys. 31, 83 (1973); ibid. 42, 281 (1975)Google Scholar
  49. 49.
    K.G. Wilson, Phys. Rev. D 10, 2445 (1974)ADSCrossRefGoogle Scholar
  50. 50.
    M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965) (Chap. 9 and formulas 9.1.39/9.1.40/9.6.4 there)Google Scholar
  51. 51.
    I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products, eds. by A. Jeffery, D. Zwanziger (Academic Press, London, 2015[1943]) (Formulas 3.471.9/11)Google Scholar
  52. 52.
    G. t’Hooft, M. Veltman, Nucl. Phys. B 153, 365 (1979)Google Scholar
  53. 53.
    A.I. Davydychev, M.Y. Kalmykov, Nucl. Phys. B 605, 266 (2001)ADSCrossRefGoogle Scholar
  54. 54.
    J. Fleischer, F. Jegerlehner, O.V. Tarasov, Nucl. Phys. B 672, 303 (2003)ADSCrossRefGoogle Scholar
  55. 55.
    J.S. Frederiksen, W.S. Woolcock, Nucl. Phys. B 28, 605 (1971); Aust. J. Phys. 26, 691 (1973); Ann. Phys. 75, 503 (1973); ibid. 80, 86 (1973)Google Scholar
  56. 56.
    G. Passarino, M. Veltman, Nucl. Phys. B 160, 151 (1979)ADSCrossRefGoogle Scholar
  57. 57.
    K.G. Chetyrkin, F.V. Tkachov, Nucl. Phys. B 192, 159 (1981)ADSCrossRefGoogle Scholar
  58. 58.
    F. Jegerlehner, Renormalizing the standard model, in Testing the Standard Model, eds. by M. Cvetič, P. Langacker (World Scientific, Singapore, 1991), pp. 476–590, http://www-com.physik.hu-berlin.de/~fjeger/books.html
  59. 59.
    F. Bloch, A. Nordsieck, Phys. Rev. D 52, 54 (1937)ADSCrossRefGoogle Scholar
  60. 60.
    Y. Hahn, W. Zimmermann, Commun. Math. Phys. 10, 330 (1968); W. Zimmermann, Commun. Math. Phys. 11, 1 (1968); J.H. Lowenstein, W. Zimmermann, Commun. Math. Phys. 44, 73 (1975)Google Scholar
  61. 61.
    F.J. Dyson, Phys. Rev. 75, 1736 (1949)ADSCrossRefGoogle Scholar
  62. 62.
    J.P. Fink, J. Math. Phys. 9, 1389 (1968); E.B. Manoukian, J. Math. Phys. 19, 917 (1978)Google Scholar
  63. 63.
    S. Weinberg, Phys. Rev. 118, 838 (1960)ADSMathSciNetCrossRefGoogle Scholar
  64. 64.
    T. Appelquist, J. Carazzone, Phys. Rev. D 11, 2856 (1975)ADSCrossRefGoogle Scholar
  65. 65.
    V.A. Smirnov, Mod. Phys. Lett. A 10, 1485 (1995) (and references therein)Google Scholar
  66. 66.
    E.C.G. Stueckelberg, A. Petermann, Helv. Phys. Acta 26, 499 (1953); M. Gell-Mann, F.E. Low, Phys. Rev. 95, 1300 (1954)Google Scholar
  67. 67.
    G. Mack, Nucl. Phys. B 5, 499 (1968)ADSCrossRefGoogle Scholar
  68. 68.
    J.D. Bjorken, Phys. Rev. 179, 1547 (1969); J.D. Bjorken, E.A. Paschos, Phys. Rev. 185, 1975 (1969)Google Scholar
  69. 69.
    D.H. Coward et al., Phys. Rev. Lett. 20, 292 (1968); E.D. Bloom et al., Phys. Rev. Lett. 23, 930 (1969); G. Miller et al., Phys. Rev. D 5, 528 (1972)Google Scholar
  70. 70.
    H. Suura, E. Wichmann, Phys. Rev. 105, 1930 (1957); A. Petermann, Phys. Rev. 105, 1931 (1957)Google Scholar
  71. 71.
    B.E. Lautrup, E. de Rafael, Nucl. Phys. B 70, 317 (1974)ADSCrossRefGoogle Scholar
  72. 72.
    E. de Rafael, J.L. Rosner, Ann. Phys. (N.Y.) 82, 369 (1974)Google Scholar
  73. 73.
    A.L. Kataev, S.A. Larin, Pisma Zh. Eksp. Teor. Fiz. 96, 64 (2012) [JETP Lett. 96, 61 (2012)]Google Scholar
  74. 74.
    P.A. Baikov, K.G. Chetyrkin, J.H. Kühn, C. Sturm, Nucl. Phys. B 867, 182 (2013)ADSCrossRefGoogle Scholar
  75. 75.
    P.A. Baikov, K.G. Chetyrkin, J.H. Kühn, J. Rittinger, JHEP 1207, 017 (2012)ADSCrossRefGoogle Scholar
  76. 76.
    D.R. Yennie, S.C. Frautschi, H. Suura, Ann. Phys. 13, 379 (1961); D.R. Yennie, Phys. Lett. 34B, 239 (1975); J.D. Jackson, D.L. Scharre, Nucl. Instr. 128, 13 (1975); M. Greco, G. Pancheri, Y. Srivastava, Nucl. Phys. B 101, 234 (1975)Google Scholar
  77. 77.
    T. Kinoshita, J. Math. Phys. 3, 650 (1962); T.D. Lee, M. Nauenberg, Phys. Rev. D 133, B1549 (1964)Google Scholar
  78. 78.
    J. Fleischer, F. Jegerlehner, Z. Phys. C 26, 629 (1985)Google Scholar
  79. 79.
    G. Sterman, S. Weinberg, Phys. Rev. Lett. 39, 1436 (1977)ADSCrossRefGoogle Scholar
  80. 80.
    O. Steinmann, Commun. Math. Phys. 237, 181 (2003)ADSCrossRefGoogle Scholar
  81. 81.
    F. Jegerlehner, Nucl. Phys. B (Proc. Suppl.) 51C, 131 (1996)Google Scholar
  82. 82.
    G.J. Gounaris, J.J. Sakurai, Phys. Rev. Lett. 21, 244 (1968); A. Quenzer et al., Phys. Lett. B 76, 512 (1978)Google Scholar
  83. 83.
    F. Jegerlehner, R. Szafron, Eur. Phys. J. C 71, 1632 (2011)ADSCrossRefGoogle Scholar
  84. 84.
    H. Leutwyler, Electromagnetic form factor of the pion, in Continuous Advances in QCD 2002: Proceedings, eds. by K.A. Olive, M.A. Shifman, M.B. Voloshin (World Scientific, Singapore, 2002), 646 p, arXiv:hep-ph/0212324
  85. 85.
    J. Gasser, H. Leutwyler, Ann. Phys. 158, 142 (1984); Nucl. Phys. B 250, 465 (1985)Google Scholar
  86. 86.
    K.G. Wilson, Phys. Rev. D 10, 2445 (1974); M. Creutz, Phys. Rev. D 21, 2308 (1980)Google Scholar
  87. 87.
    Y. Nambu, Phys. Rev. Lett. 4, 380 (1960)ADSCrossRefGoogle Scholar
  88. 88.
    G. ’t Hooft, Nucl. Phys. B 72, 461 (1974); ibid. 75, 461 (1974); E. Witten, Nucl. Phys. B 160, 57 (1979)Google Scholar
  89. 89.
    A.V. Manohar, Hadrons in the \(1/N\) expansion, in At the frontier of Particle Physics, vol. 1, ed. M. Shifman (World Scientific, Singapore, 2001)pp. 507–568Google Scholar
  90. 90.
    H. Leutwyler, Nucl. Phys. Proc. Suppl. 64, 223 (1998); R. Kaiser, H. Leutwyler, Eur. Phys. J. C 17, 623 (2000)Google Scholar
  91. 91.
    S. Okubo, Phys. Lett. 5, 1975 (1963); G. Zweig, CERN Report No.8419/TH412 (1964); J. Iizuka. Prog. Theor. Phys. Suppl. 37, 38 (1966)Google Scholar
  92. 92.
    S.L. Glashow, Phys. Rev. Lett. 7, 469 (1961)ADSCrossRefGoogle Scholar
  93. 93.
    S. Okubo, Phys. Lett. 5, 165 (1963)ADSCrossRefGoogle Scholar
  94. 94.
    W.E. Caswell, Phys. Rev. Lett. 33, 244 (1974); D.R.T. Jones, Nucl. Phys. B 75, 531 (1974); E. Egorian, O.V. Tarasov, Theor. Math. Phys. 41, 863 (1979) [Teor. Mat. Fiz. 41, 26 (1979)]Google Scholar
  95. 95.
    O.V. Tarasov, A.A. Vladimirov, A.Y. Zharkov, Phys. Lett. B 93, 429 (1980); S.A. Larin, J.A.M. Vermaseren, Phys. Lett. B 303, 334 (1993)Google Scholar
  96. 96.
    T. van Ritbergen, J.A.M. Vermaseren, S.A. Larin, Phys. Lett. B 400, 379 (1997); M. Czakon, Nucl. Phys. B 710, 485 (2005); K.G. Chetyrkin, Nucl. Phys. B 710, 499 (2005)Google Scholar
  97. 97.
    P.A. Baikov, K.G. Chetyrkin, J.H. Kühn, Phys. Rev. Lett. 118, 082002 (2017)ADSCrossRefGoogle Scholar
  98. 98.
    S. Bethke, Phys. Rep. 403–404, 203 (2004)CrossRefGoogle Scholar
  99. 99.
    K.A. Olive et al. (Particle Data Group), Chin. Phys. C 38, 090001 (2014); Quantum Chromodynamics eds. by S. Bethke, G. Dissertori, G.P. Salam (therein)Google Scholar
  100. 100.
    M. Della Morte, R. Frezzotti, J. Heitger, J. Rolf, R. Sommer, U. Wolff, Nucl. Phys. B 713, 378 (2005)ADSCrossRefGoogle Scholar
  101. 101.
    F. Tekin et al. [ALPHA Collab.], Nucl. Phys. B 840, 114 (2010)Google Scholar
  102. 102.
    M. Dalla Brida et al. [ALPHA Collab.], Phys. Rev. D 95, 014507 (2017)Google Scholar
  103. 103.
    M. Bruno et al., Nucl. Part. Phys. Proc. 285–286, 132 (2016); PoS Lattice 2016, 197 (2016), arXiv:1701.03075 [hep-lat]
  104. 104.
    F. Jegerlehner, Acta Phys. Polon. B 45, 1167 (2014)ADSMathSciNetCrossRefGoogle Scholar

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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institut für PhysikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Deutsches Elektronen-Synchrotron (DESY)ZeuthenGermany

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