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Part of the book series: Springer Series on Atomic, Optical, and Plasma Physics ((SSAOPP,volume 40))

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Abstract

Quantum electrodynamics (QED), the study of the motion of electrically charged particles such as electrons, positrons, and charged nuclei, provides the formal framework for the relativistic theory of atoms, molecules, and other forms of matter. Quantum field theory [1, 2], of which QED is an example, was invented to model physical processes in which the number of particles is not necessarily fixed. The coupling of the electron-positron field with the Maxwell photon field in QED allows us to build a relativistic theory of atoms and molecules. Feynman diagrams serve to clarify the radiative and collision processes that contribute to atomic and molecular physics. A subset of these diagrams corresponds to the familiar self-consistent field theory, which is both the starting point for more accurate calculations as well as a popular model in its own right. Diagrams associated with “radiative corrections”, which are not normally included in theories of atomic or molecular electronic structure, pose additional technical challenges. The interaction of a charged particle with the fluctuations of the Maxwell photon field leads to a correction to the particle’s energy and to its magnetic moment, whilst the particle’s charge modifies the electromagnetic field close by. These radiative corrections can be significant in some applications.

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References

  1. Schweber S S 1961 An Introduction to Relativistic Quantum Field Theory (New York: Harper & Row).

    Google Scholar 

  2. Itzykson C and Zuber J-B 1980 Quantum Field Theory (New York: McGraw-Hill Book Company).

    Google Scholar 

  3. Hamermesh M, 1962 Group Theory (Reading, Mass.: Addison-Wesley Publishing Co. Inc.).

    MATH  Google Scholar 

  4. Elliott J P and Dawber P G 1979 Symmetry in Physics (Basingstoke: Macmillan Press).

    Google Scholar 

  5. Furry W H 1951 ai]Phys._Rev. 81 115.

    Google Scholar 

  6. Thaller B 1992 The Dirac Equation (Berlin: Springer-Verlag).

    Google Scholar 

  7. Schweber S S 1994 QED and the men who made it: Dyson, Feynman, Schwinger and Tomonaga (Princeton NJ: Princeton University Press).

    MATH  Google Scholar 

  8. Greiner W, Müller B and Rafelski J 1985 Quantum Electrodynamics of Strong Fields (Berlin: Springer-Verlag).

    Google Scholar 

  9. Gupta S N 1950 Proc. Phys. Soc. (London) A63, 681.

    ADS  Google Scholar 

  10. Bleuler K 1950 Helv. Phys. Acta 23, 567.

    MATH  MathSciNet  Google Scholar 

  11. Plunien G, Müller B, Greiner W and Soff G 1989 Phys Rev A 39 5428.

    ADS  Google Scholar 

  12. Plunien G, Müller B, Greiner W and Soff G 1991 Phys Rev A 43 5853.

    ADS  Google Scholar 

  13. Bar-Shalom A, Klapisch M and Oreg J 2001 J. Quant. Spectrosc. Rad. Transf. 71, 169.

    ADS  Google Scholar 

  14. Stakgold 1979 Green’s functions and Boundary Value Problems (New York: John Wiley & Sons).

    MATH  Google Scholar 

  15. Dyson, F J 1951 Phys. Rev. 82 428.

    MATH  ADS  MathSciNet  Google Scholar 

  16. Dyson, F J 1951 Phys. Rev. 83 608.

    MATH  ADS  MathSciNet  Google Scholar 

  17. Wick G C1950 Phys. Rev. 80 268.

    MATH  ADS  MathSciNet  Google Scholar 

  18. Feynman R P 1949 Phys Rev 76 749, 769.

    MATH  ADS  MathSciNet  Google Scholar 

  19. Gell-Mann M and Low F, 1951 Phys. Rev. 84 350.

    MATH  ADS  MathSciNet  Google Scholar 

  20. Sucher J 1957 Phys. Rev. 107 1448.

    ADS  MathSciNet  Google Scholar 

  21. Lindgren I 1989 in Relativistic, Quantum Electrodynamic and Weak Interaction Effects in Atoms (ed. W R Johnson, P J Mohr and J Sucher), pp. 371–392 (New York: American Institute of Physics).

    Google Scholar 

  22. MØller C 1932 Ann. der Phys. 14 531.

    MATH  Google Scholar 

  23. Gaunt J A Proc. Roy. Soc. A 122 513.

    Google Scholar 

  24. Bethe H A and Salpeter E E 1957 Quantum Mechanics of One-and Two-Electron Atoms (Berlin-Göttingen-Heidelberg: Springer-Verlag).

    MATH  Google Scholar 

  25. Gradshteyn I S and Ryzhik I M 1980 Table of Integrals, Series and Products (4th edition, ed. A Jeffrey) (London: Academic Press).

    Google Scholar 

  26. Brueckner K A and Levinson C A1955 Phys. Rev. 97, 1344.

    MATH  ADS  Google Scholar 

  27. Bethe H A 1956 Phys. Rev. 103, 1353.

    MATH  ADS  Google Scholar 

  28. Eden R J 1956 Proc. Roy. Soc. A 235, 408.

    MATH  ADS  Google Scholar 

  29. Brueckner K A 1955 Phys. Rev. 97, 1353.

    MATH  ADS  Google Scholar 

  30. Brueckner K A 1955 Phys. Rev. 100, 36.

    MATH  ADS  Google Scholar 

  31. Goldstone J 1957 Proc. Roy. Soc. A 239 267.

    MATH  ADS  MathSciNet  Google Scholar 

  32. Kelly H P 1963 Phys. Rev. 131, 684.

    MATH  ADS  Google Scholar 

  33. Kelly H P and Sessler A M 1963 Phys. Rev. 132, 2091.

    MATH  ADS  Google Scholar 

  34. Kelly H P 1964 Phys. Rev. 134, A1450.

    ADS  Google Scholar 

  35. Kelly H P 1964 Phys. Rev. 136, B896.

    ADS  Google Scholar 

  36. Brandow H B 1967 ai]Rev._Mod. Phys. 39, 771.

    Google Scholar 

  37. Brandow H B 1977 Adv. Quantum Chem. 10, 187.

    ADS  Google Scholar 

  38. Sandars P G H 1967 in La Structure Hyperfine Magnétique des Atomes et des Molècules (Paris: CNRS).

    Google Scholar 

  39. Yutsys AP Levinson I B and Vanagas V V 1962 Mathematical Apparatus of the Theory of Anglar Momentum (Jerusalem: Israel Program for Scientific Translations).

    Google Scholar 

  40. Lindgren I and Morrison J 1982 Atomic Many-Body Theory (Berlin: Springer-Verlag).

    Google Scholar 

  41. Lindgren I 1974 J. Phys. B 7, 2441.

    ADS  Google Scholar 

  42. KvasnÏcka V1974 Czech. J. Phys. B 24, 605; see also KvasnÏcka V 1977 in Adv. in Chem. Phys. Vol. 36 (ed. Prigogine I and Rice S A), p.345. (New York: Interscience).

    Google Scholar 

  43. Boyle J J and Pindzola M S 1998 Many-body atomic physics (Cambridge University Press).

    Google Scholar 

  44. Wilson S 1984 Electron correlation in molecules (Oxford: Clarendon Press).

    Google Scholar 

  45. Brown G E and Ravenhall D G 1951 Proc. Roy. Soc. A 208, 552.

    MATH  ADS  MathSciNet  Google Scholar 

  46. Breit G 1929 Phys Rev 34 353; — 1930 Phys Rev 36 383; — 1932 Phys Rev 39 616.

    ADS  Google Scholar 

  47. Sucher J 1980 Phys. Rev. A 22, 348.

    ADS  MathSciNet  Google Scholar 

  48. Sucher J 1980 in Proceedings of the Argonne Workshop on the Relativistic Theory of Atomic Structure, ed. H G Berry, K T Cheng, W R Johnson and Y-K Kim. ANL-80-116 (Argonne National Laboratory).

    Google Scholar 

  49. Sucher J 1982 Relativistic Effects in Atoms, Molecules and Solids, ed. G L Malli, pp. 1–53. (NATO ASI, Series B: Vol. 87) (New York, Plenum).

    Google Scholar 

  50. Sucher J 1984 Int. J. Quant. Chem. 25, 3.

    Google Scholar 

  51. Sucher J 1985 Atomic Theory Workshop on Relativistic and QED Effects in Heavy Atoms, ed. H P Kelly and Y-K Kim. pp. 1–25 (AIP Conference Series No. 136) (New York, American Insitute of Physics).

    Google Scholar 

  52. Sapirstein J 1998 Rev. Mod. Phys. 70, 55.

    ADS  Google Scholar 

  53. Rossky P and Karplus M 1977 J. Chem. Phys. 67, 5419.

    ADS  MathSciNet  Google Scholar 

  54. Quiney H M, Grant I P and Wilson S 1985 J. Phys. B 18, 577.

    ADS  Google Scholar 

  55. Quiney H M, Grant I P and Wilson S 1985 J. Phys. B 18, 2805.

    ADS  Google Scholar 

  56. Grant I P and Quiney H M 2000 Phys. Rev. A 62, 022508.

    ADS  Google Scholar 

  57. Malli G L (ed.) 1983 Relativistic Effects in Atoms, Molecules and Solids (NATO Advanced Study Institutes, Series B., Physics, Vol. 87) (New York: Plenum Press).

    Google Scholar 

  58. Schwarz W H E and Wallmeier H 1982 Mol. Phys. 46, 1045.

    ADS  Google Scholar 

  59. Schwarz W H E and Wechsel-Trakowski E 1982 Chem. Phys. Lett. 85, 94.

    ADS  Google Scholar 

  60. Wallmeier H and Kutzelnigg W 1981 Chem. Phys. Lett. 78, 341.

    ADS  Google Scholar 

  61. Mark F and Rosicky F 1980 Chem. Phys. Lett. 74, 562.

    ADS  MathSciNet  Google Scholar 

  62. Mark F and Schwarz W H E 1982 Phys. Rev. Lett. 48, 673.

    ADS  Google Scholar 

  63. Grant I P and Quiney H M 2000 Int. J. Quant. Chem¿ 80 283.

    Google Scholar 

  64. Kutzelnigg W 1984 Int. J. Quant. Chem. 25, 107.

    Google Scholar 

  65. Foldy L L and Wouthuysen S A 1950 Phys. Rev. 78 29.

    MATH  ADS  Google Scholar 

  66. Douglas M and Kroll N M 1974 Ann Phys (NY) 82 89.

    ADS  Google Scholar 

  67. Hess B A 1986 Phys Rev A 32 756; Phys Rev A 33 3742.

    ADS  Google Scholar 

  68. Chang Ch., Pélissier M and Durand P 1986 Phys. Scr. 34, 394.

    ADS  Google Scholar 

  69. van Lenthe E, Baerends E-J and Snijders J G 1993 J. Chem. Phys. 99, 4597.

    ADS  Google Scholar 

  70. van Lenthe E, van Leeuven R, Baerends E-J and Snijders J G 1996 Int. J. Quant. Chem. 57, 281.

    Google Scholar 

  71. Karshenboim S G, Pavone F S, Bassani F, Inguscio M and HÄnsch TW 2001 The Hydrogen Atom. Precision Physics of Simple Atomic systems (Berlin: Springer-Verlag).

    Google Scholar 

  72. Quiney H M, Grant I P and Wilson S 1989, in Many-Body Methods in Quantum Chemistry (Lecture Notes in Chemistry 52) ed. U Kaldor pp. 307–344 (Berlin: Springer-Verlag).

    Google Scholar 

  73. Sapirstein J, Cheng K T and Chen M H 1999 Phys. Rev. A 59 259.

    ADS  Google Scholar 

  74. Bishop R and Kummel H 1987 Phys. Today 40, 42.

    Google Scholar 

  75. Bartlett R J 1991 Theor. Chim. Acta 80, 71.

    Google Scholar 

  76. Paldus J 1992 in Methods in Computational Molecular Physics (ed. S Wilson and G H F Diercksen) pp. 99–194, (NATO ASI Series B: Physics Vol. 293) (New York: Plenum Press).

    Google Scholar 

  77. Lawley K P (ed.) 1987 Adv. Chem. Phys. 69 (New York: John Wiley).

    Google Scholar 

  78. Fischer C F, Brage T and Jönsson P 1997 Computational Atomic Structure. An MCHF approach (Bristol and Philadelphia: Institute of Physics).

    Google Scholar 

  79. Desclaux J-P 1975 Comput. Phys. Commun. 9, 31.

    ADS  Google Scholar 

  80. Grant I P, McKenzie B J, Norrington P H, Mayers DF and Pyper N C 1980 Comput. Phys. Commun. 21, 207.

    ADS  Google Scholar 

  81. Dyall K G, Grant I P, Johnson C T and Plummer E P 1989 Comput. Phys. Commun. 55, 425.

    ADS  Google Scholar 

  82. Parpia F A, Fischer C F and Grant I P 1996 Comput. Phys. Commun. 94, 249.

    ADS  Google Scholar 

  83. Jensen H J A, Dyall K G, Saue T, FÆri K 1996 J. Chem. Phys. 104, 4083.

    ADS  Google Scholar 

  84. Saue T and Jensen H J A 1999 J. Chem. Phys. 111, 6211.

    ADS  Google Scholar 

  85. Quiney H M, Skaane H and Grant I P 1998 Chem. Phys. Lett. 290, 473.

    ADS  Google Scholar 

  86. Quiney H M, Skaane H and Grant I P 1999 Adv. Quant. Chem. 32, 1.

    Google Scholar 

  87. Quiney H M 2002 in Handbook of Molecular Physics and Quantum Chemistry (Chichester: John Wiley).

    Google Scholar 

  88. Grant I P and Quiney H M 2002 in Relativistic Quantum Chemistry (ed. P Schwerdtfeger) pp. 107–202 (Amsterdam: Elsevier).

    Google Scholar 

  89. Rajagopal A K and Callaway J 1973 Phys. Rev. B 59, 1912.

    ADS  Google Scholar 

  90. Rajagopal A K 1978 J. Phys. C 11, L943.

    ADS  Google Scholar 

  91. Macdonald A H and Vosko S H 1979 J. Phys. C 12, 2977.

    ADS  Google Scholar 

  92. Dreizler R M and Gross E K U 1990 Density Functional Theory (Berlin:: Springer-Verlag).

    MATH  Google Scholar 

  93. Engel E and Dreizler R M 1996 Topics in Current Chem. 181, 1.

    Google Scholar 

  94. Engel E, Facco Bonetti A, Keller S, Andrejkocics I and Dreizler R M 1998 Phys. Rev. A 58, 964.

    ADS  Google Scholar 

  95. Engel E and Dreizler R M 1999 J. Comp. Chem. 20, 31.

    Google Scholar 

  96. Engel E, Dreizler R M, Varga S and Fricke B 2003 in Relativistic Effects in Heavy Element Chemistry and Physics (ed. B A Hess), Chapter 4. Relativistic Density Functional Theory. (Chichester: John Wiley and Sons, Ltd.).

    Google Scholar 

  97. Engel E 2002 in Relativistic Quantum Chemistry (ed. P Schwerdtfeger) pp. 523–621. (Amsterdam: Elsevier).

    Google Scholar 

  98. Hohenberg P and Kohn W 1964 Phys. Rev. 136 B, 864.

    ADS  MathSciNet  Google Scholar 

  99. Thomas L H 1927 Proc. Camb. Phil. Soc. 23, 542.

    MATH  Google Scholar 

  100. Fermi E 1928 Z. Physik 48, 73.

    ADS  Google Scholar 

  101. Slater J C 1951 Phys. Rev. 81, 385.

    MATH  ADS  Google Scholar 

  102. Akhiezer I A and Peletminskii SV 1960 Zh. Eksp. Teor. Fiz. 38, 1829 [Sov. Phys. JETP 11, 1318.]

    Google Scholar 

  103. Becke A D 1988 Phys. Rev. A 38, 3098.

    ADS  Google Scholar 

  104. Perdew J P, Chevary J A, Vosko S H, Jackson K A, Pederson M R, Singh D J and Fiolhais C1992 Phys. Rev. B 46, 6671.

    ADS  Google Scholar 

  105. Engel E, Keller S and Dreizler R M 1996 Phys. Rev. A 53, 1367.

    ADS  Google Scholar 

  106. Engel E, Keller S and Dreizler R M 1998 in Electronic Density Functional Theory: Recent Progress and New Directions (ed J F Dobson, G Vignals and M P Das), p. 149 (New York: Plenum).

    Google Scholar 

  107. Kim Y-H, StÄdele M and Martin R M 1999 Phys. Rev. A 60, 3633.

    ADS  Google Scholar 

  108. Sham L J 1985 Phys. Rev. B 32, 3876.

    ADS  Google Scholar 

  109. Görling A and Levy M 1994 Phys. Rev. A 50, 196.

    ADS  Google Scholar 

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(2007). Quantum electrodynamics. In: Grant, I.P. (eds) Relativistic Quantum Theory of Atoms and Molecules. Springer Series on Atomic, Optical, and Plasma Physics, vol 40. Springer, New York, NY. https://doi.org/10.1007/978-0-387-35069-1_4

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