Heisenberg-euler effective lagrangians: Basics and extensions

From Fields to Strings: Circumnavigating Theoretical Physics: Ian Kogan Memorial Collection

Volumn 1, Issue , 2005, Pages 445-522

  Dunne, Gerald V ^a  

^a UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

QUANTUM ELECTRONICS;

BACKGROUND FIELD; HEISENBERG; QUANTUM ELECTRODYNAMICS;

ELECTRODYNAMICS;

EID: 85014659898     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9789812775344_0014     Document Type: Chapter

References (184)

1. W. Heisenberg and H. Euler, Z. Phys. 98, 714 (1936).
2. V. Weisskopf, Kong. Dans. Vid. Selsk. Math-fys. Medd. XIV No. 6 (1936).
3. English translation in: Early Quantum Electrodynamics: A Source Book, A. I. Miller, (Cambridge University Press, 1994).
4. U. D. Jentschura, H. Gies, S. R. Valluri, D. R. Lamm and E. J. Weniger, Can. J. Phys. 80, 267 (2002) [hep-th/0107135].
5. W. Greiner and J. Reinhardt, Quantum Electrodynamics, (Springer, Berlin, 1992).
6. W. Greiner, B. Muller and J. Rafelski, Quantum Electrodynamics Of Strong Fields, (Springer, Berlin, 1985).
7. W. Dittrich and M. Reuter, Effective Lagrangians In Quantum Electrodynamics, Lect. Notes Phys. 220, 1 (Springer, Berlin, 1985).
8. S. K. Blau, M. Visser and A. Wipf, Int. J. Mod. Phys. A 6, 5409 (1991).
9. R. Soldati and L. Sorbo, Phys. Lett. B 426, 82 (1998) [hep-th/9802167].
10. W. Dittrich and H. Gies, Probing the quantum vacuum. Perturbative effective action approach in quantum electrodynamics and its application, Springer Tracts Mod. Phys. 166, 1 (2000).
11. H. Euler and B Kockel, Naturwiss. 23, 246 (1935).
12. R. Karplus and M. Neuman, Phys. Rev. 83, 776 (1951).
13. F. Sauter, Zeit. f. Phys. 69, 742 (1931).
14. J. Schwinger, Phys. Rev. 82 (1951) 664.
15. J. Schwinger, Phys. Rev. 93, 615 (1954); Phys. Rev. 94, 1362 (1954).
16. A. Ringwald, Phys. Lett. B 510, 107 (2001) [hep-ph/0103185]
17. Fundamental physics at an X-ray free electron laser, in Proceedings of Erice Workshop On Electromagnetic Probes Of Fundamental Physics, W. Marciano and S. White (Eds.), (River Edge, World Scientific, 2003) [hep-ph/0112254].
18. V. Weisskopf, Phys. Rev. 56, 72 (1939).
19. M. Gell-Mann and F. E. Low, Phys. Rev. 95, 1300 (1954).
20. A. V. Manohar, Effective field theories, in Proceedings of Schladming Winter School Perturbative And Nonperturbative Aspects Of Quantum Field Theory, Eds. H. Latal and W. Schweiger, (Springer-Verlag, Berlin, 1997) [hep-ph/9606222].
21. J. F. Donoghue, E. Golowich and B. R. Holstein, Dynamics Of The Standard Model, (Cambridge University Press, 1992).
22. V. A. Novikov, M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Fortsch. Phys. 32, 585 (1985).
23. M. A. Shifman, ITEP Lectures On Particle Physics And Field Theory. Vol. 1, 2, World Sci. Lect. Notes Phys. 62, 1 (1999).
24. V.A. Novikov, M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Nucl. Phys. B 174, 378 (1980); Nucl. Phys. B 249, 445 (1985) [Yad. Fiz. 41, 1063 (1985)].
25. A. Erdelyi (ed.), Higher Transcendental Functions, Vol. I, (Kreiger, Florida, 1981).
26. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, (Dover, New York, 1972).
27. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series and Products, (Academic Press, New York, 1972).
28. E. Whittaker and G. Watson, Modern Analysis, (Cambridge, 1927).
29. S. Chadha and P. Olesen, Phys. Lett. B 72, 87 (1977).
30. B. C. Berndt (Ed.), Ramanujan’s Notebooks, Vol. II, (Springer, New York, 1985).
31. S. R. Valluri, D. R. Lamm and W. J. Mielniczuk, Can. J. Phys. 71, 389 (1993).
32. A.I. Nikishov, Zh. Eksp. Teor. Fiz. 57, 1210 (1969) [Sov. Phys. JETP 30, 660 (1970)].
33. V. S. Popov, Sov. Phys. JETP 34, 709 (1972); Sov. Phys. JETP 35, 659 (1972).
34. E. Elizalde, Ten Physical Applications Of Spectral Zeta Functions, Lect. Notes Phys. M35, (Springer-Verlag, Berlin, 1995).
35. K. Kirsten, Spectral Functions in Mathematics and Physics, (Chapman-Hall, Boca Raton, 2002).
36. E.W. Barnes, Quart. J. Pure Appl. Math XXXI, 264 (1900).
37. V. Adamchik, Symbolic and Numeric computation of the Barnes function, Conference on Applications of Computer Algebra, Albuquerque, June 2001; Contributions to the theory of the Barnes function, math.CA/0308086.
38. A. Salam and P. T. Matthews, Phys. Rev. 90, 690 (1953).
39. A. Salam and J. Strathdee, Nucl. Phys. B 90, 203 (1975).
40. D. M. Volkov, Z. Phys. 94, 25 (1935).
41. V.B. Berestetskii, E.M. Lifshitz, and L.P. Pitaevskii, Quantum electrodynamics, (Pergamon Press, New York, 1982).
42. L. S. Brown and T. W. B. Kibble, Phys. Rev. 133, A705 (1964).
43. F. V. Bunkin and I. I. Tugov, Sov. Phys. Dokl. 14 (1970), 678.
44. H. M. Pried, Y. Gabellini, B. H. J. McKellar and J. Avan, Phys. Rev. D 63, 125001 (2001).
45. N.B. Narozhnyi and A.I. Nikishov, Yad. Fiz. 11, 1072 (1970) [Sov. J. Nucl. Phys. 11 (1970) 596].
46. G. V. Dunne and T. Hall, Phys. Rev. D 58, 105022 (1998) [hep-th/9807031].
47. D. Cangemi, E. D’Hoker and G. V. Dunne, Phys. Rev. D 52, 3163 (1995) [hep-th/9506085].
48. G. V. Dunne and T. M. Hall, Phys. Lett. B 419, 322 (1998) [hep-th/9710062].
49. S. P. Kim and D. N. Page, Phys. Rev. D 65, 105002 (2002) [hep-th/0005078].
50. A. I. Nikishov, On the theory of scalar pair production by a potential barrier, hep-th/0111137.
51. H. J. de Vega and F. A. Schaposnik, Phys. Rev. D 26, 2814 (1982).
52. T. N. Tomaras, N. C. Tsamis and R. P. Woodard, Phys. Rev. D 62, 125005 (2000) [hep-ph/0007166]; JHEP 0111, 008 (2001) [hep-th/0108090].
53. H. M. Fried and R. P. Woodard, Phys. Lett. B 524, 233 (2002) [hep-th/0110180].
54. E. Brezin and C. Itzykson, Phys. Rev. D 2, 1191 (1970).
55. V. S. Popov and M. S. Marinov, Yad. Fiz. 16, 809 (1972), [Sov. J. Nucl. Phys. 16 (1973), 449]; Fortsch. Phys. 25, 373 (1977).
56. L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).
57. A. M. Perelomov, V. S. Popov and M. V. Terent’ev, Sov. Phys JETP 23, 924 (1966), 24, 207 (1967).
58. L.D. Landau and E.M. Lifshitz, Quantum mechanics: non-relativistic theory, (Pergamon Press, New York, 1977).
59. J. R. Oppenheimer, Phys. Rev. 31, 66 (1928).
60. CM. Bender and S.A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, (Mc Graw-Hill, New York, 1978).
61. M. J. Strassler, Nucl. Phys. B 385, 145 (1992) [hep-ph/9205205].
62. M.G. Schmidt, C. Schubert, Phys. Lett. B 318, 438 (1993) [hep-th/9309055].
63. M. G. Schmidt and C. Schubert, Phys. Lett. B 331 (1994) 69 [hep-th/9403158]; Phys. Rev. D 53, 2150 (1996) [hep-th/9410100].
64. D.G.C. McKeon and T.N. Sherry, Mod. Phys. Lett. A 9, 2167 (1994).
65. C. Schubert, Phys. Rept. 355 (2001) 73 [hep-th/0101036].
66. D. Cangemi, E. D’Hoker and G. V. Dunne, Phys. Rev. D 51, 2513 (1995) [hep-th/9409113].
67. H. W. Lee, P. Y. Pac and H. K. Shin, Phys. Rev. D 40, 4202 (1989).
68. V. P. Gusynin and I. A. Shovkovy, Can. J. Phys. 74, 282 (1996) [hep-ph/9509383]; J. Math. Phys. 40, 5406 (1999) [hep-th/9804143].
69. G. V. Dunne and T. M. Hall, Phys. Rev. D 60, 065002 (1999) [hep-th/9902064].
70. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, (Oxford University Press, 1997).
71. G. ‘t Hooft, Can we make sense out of ‘quantum chromodynamics’? in The Whys of Subnuclear Physics, ed. A. Zichichi, (Plenum, New York, 1978); Reprinted in: G. ‘t Hooft, Under the spell of the gauge principle, (World Scientific, Singapore, 1994).
72. D. Fliegner, P. Haberl, M. G. Schmidt and C. Schubert, Nucl. Instrum. Meth. A 389, 374 (1997) [hep-th/9702092]; Annals Phys. 264, 51 (1998) [hep-th/9707189].
73. U. Muller, A basis for invariants in non-Abelian gauge theories, hep-th/9508031.
74. J. A. M. Vermaseren, New features of FORM, math-ph/0010025.
75. A. E. M. van de Ven, Class. Quant. Grav. 15, 2311 (1998) [hep-th/9708152].
76. H. Gies and K. Langfeld, Nucl. Phys. B 613, 353 (2001) [hep-ph/0102185]; Int. J. Mod. Phys. A 17, 966 (2002) [hep-ph/0112198]
77. K. Langfeld, L. Moyaerts and H. Gies, Nucl. Phys. B 646, 158 (2002) [hep-th/0205304].
78. M. G. Schmidt and I. O. Stamatescu, Determinant calculations with random walk worldline loops, hep-lat/0201002; Mod. Phys. Lett. A 18, 1499 (2003); Nucl. Phys. Proc. Suppl. 119, 1030 (2003) [hep-lat/0209120].
79. H. Gies, K. Langfeld and L. Moyaerts, JHEP 0306, 018 (2003) [hep-th/0303264].
80. M. P. Pry, Phys. Rev. D 54, 6444 (1996) [hep-th/9606037]; Int. J. Mod. Phys. A 17, 936 (2002) [hep-th/0111244]; Phys. Rev. D 67, 065017 (2003) [hep-th/0301097]; Fermion determinants 2003, To appear in the proceedings of 6th Workshop on Quantum Field Theory under the Influence of External Conditions (QFEXT03), Norman, Oklahoma, Sep 2003, [hep-th/0311145].
81. V. S. Vanyashin and M. V. Terentev, Sov. Phys. JETP 21, 375 (1965).
82. D. J. Gross and F. Wilczek, Phys. Rev. Lett. 30, 1343 (1973); Phys. Rev. D 8, 3633 (1973); Phys. Rev. D 9, 980 (1974).
83. H. D. Politzer, Phys. Rev. Lett. 30, 1346 (1973).
84. V. V. Skalozub, Sov. J. Nucl. Phys. 21, 690 (1976).
85. M. R. Brown and M. J. Duff, Phys. Rev. D 11, 2124 (1975).
86. I. A. Batalin, S. G. Matinyan and G. K. Savvidy, Sov. J. Nucl. Phys. 26, 214 (1977) [Yad. Fiz. 26, 407 (1977)].
87. G. M. Shore, Annals Phys. 137, 262 (1981).
88. M. J. Duff and M. Ramon-Medrano, Phys. Rev. D 12, 3357 (1975).
89. G. K. Savvidy, Phys. Lett. B 71, 133 (1977).
90. S. G. Matinyan and G. K. Savvidy, Nucl. Phys. B 134, 539 (1978).
91. S. R. Coleman and E. Weinberg, Phys. Rev. D 7, 1888 (1973).
92. V. I. Ritus, Zh. Eksp. Teor. Fiz 69, 1517 (1975) [Sov. Phys. JETP 42, 774 (1975)].
93. V. I. Ritus, Zh. Eksp. Teor. Fiz 73, 807 (1977) [Sov. Phys. JETP 46, 423 (1977)].
94. V. I. Ritus, The Lagrangian Function of an Intense Electromagnetic Field, in Proc. Lebedev Phys. Inst. Vol. 168, Issues in Intense-field Quantum Electrodynamics, V.I. Ginzburg, ed., (Nova Science Pub., NY 1987); Effective Lagrange function of intense electromagnetic field in QED, hep-th/9812124.
95. W. Y. Tsai and A. Yildiz, Phys. Rev. D 4, 3643 (1971).
96. T. Goldman, W. Y. Tsai and A. Yildiz, Phys. Rev. D 5, 1926 (1972).
97. N. K. Nielsen and P. Olesen, Nucl. Phys. B 144, 376 (1978); Phys. Lett. B 79, 304 (1978).
98. H. B. Nielsen and P. Olesen, Nucl. Phys. B 160, 380 (1979).
99. J. Ambjorn and P. Olesen, Nucl. Phys. B 170, 265 (1980).
100. P. Olesen, Phys. Scripta 23, 1000 (1981).
101. A. Yildiz and P. H. Cox, Phys. Rev. D 21, 1095 (1980).
102. M. Claudson, A. Yildiz and P. H. Cox, Phys. Rev. D 22, 2022 (1980).
103. H. Leutwyler, Phys. Lett. B 96, 154 (1980); Nucl. Phys. B 179, 129 (1981).
104. M. J. Duff and C. J. Isham, Phys. Lett. B 86, 157 (1979).
105. M. J. Duff and C. J. Isham, Nucl. Phys. B 162, 271 (1980).
106. M. T. Grisaru and H. N. Pendleton, Nucl. Phys. B 124, 81 (1977).
107. M. T. Grisaru, H. N. Pendleton and P. van Nieuwenhuizen, Phys. Rev. D 15, 996 (1977).
108. S. M. Christensen, S. Deser, M. J. Duff and M. T. Grisaru, Phys. Lett. B 84, 411 (1979).
109. R. E. Kallosh, JETP Lett. 29, 172 (1979) [Pisma Zh. Eksp. Teor. Fiz. 29, 192 (1979)]; JETP Lett. 29, 449 (1979) [Pisma Zh. Eksp. Teor. Fiz. 29, 493 (1979)].
110. W. Dittrich and M. Reuter, Phys. Lett. B 128, 321 (1983).
111. E. Elizalde, Nucl. Phys. B 243, 398 (1984).
112. E. Elizalde and J. Soto, Annals Phys. 162, 192 (1985).
113. E. Elizalde and J. Soto, Nucl. Phys. B 260, 136 (1985).
114. T. D. Gargett and I. N. McArthur, J. Math. Phys. 39, 4430 (1998).
115. S. M. Kuzenko and I. N. McArthur, JHEP 0305, 015 (2003) [hep-th/0302205].
116. M. Reuter, M. G. Schmidt and C. Schubert, Annals Phys. 259, 313 (1997) [hep-th/9610191].
117. I. L. Buchbinder and S. M. Kuzenko, Ideas And Methods Of Supersymmetry And Supergravity: Or A Walk Through Superspace, (IOP Press, Bristol, 1998).
118. E.S. Fradkin, A.A. Tseytlin, Nucl. Phys. B 227, 252 (1983).
119. I. L. Buchbinder, S. M. Kuzenko and A. A. Tseytlin, Phys. Rev. D 62, 045001 (2000) [hep-th/9911221].
120. G. ‘t Hooft, Phys. Rev. D 14, 3432 (1976) [Erratum-ibid. D 18, 2199 (1978)].
121. R. Jackiw and C. Rebbi, Phys. Lett. B 67, 189 (1977); Phys. Rev. D 16, 1052 (1977).
122. A. S. Schwarz, Phys. Lett. B 67, 172 (1977).
123. A. D’Adda and P. Di Vecchia, Phys. Lett. B 73, 162 (1978).
124. R. D. Carlitz and D. B. Creamer, Annals Phys. 118, 429 (1979).
125. O. K. Kwon, C. Lee and H. Min, Phys. Rev. D 62, 114022 (2000) [hep-ph/0008028].
126. D. J. Gross, R. D. Pisarski and L. G. Yaffe, Rev. Mod. Phys. 53, 43 (1981).
127. D. Diakonov, N. Gromov, V. Petrov and S. Slizovskiy, Quantum weights of dyons and of instantons with non-trivial holonomy, hep-th/0404042.
128. G. V. Dunne, A. W. Thomas and S. V. Wright, Phys. Lett. B 531, 77 (2002) [hep-th/0110155].
129. V. Fock, Phys. Z. Sow. 12, 404 (1937).
130. Y. Nambu, Prog. Theor. Phys. 5, 82 (1950).
131. C. Itzykson, J. Zuber, Quantum Field Theory, (McGraw-Hill, 1985).
132. G. V. Dunne and C. Schubert, Nucl. Phys. B 564, 591 (2000) [hep-th/9907190].
133. S. L. Lebedev and V. I. Ritus, Sov. Phys. JETP 59, 237 (1984) [Zh. Eksp. Teor. Fiz. 86, 408 (1984)].
134. V. I. Ritus, Sov. Phys. JETP 48, 788 (1978) [Zh. Eksp. Teor. Fiz. 75, 1560 (1978)].
135. I. K. Affleck, O. Alvarez and N. S. Manton, Nucl. Phys. B 197, 509 (1982).
136. W. Dittrich, J. Phys. A 10, 833 (1977).
137. D. Fliegner, M. Reuter, M. G. Schmidt, C. Schubert, Teor. Mat. Fiz. 113 (1997) 289 [Theor. Math. Phys. 113 (1997) 1442] [hep-th/9704194].
138. B. KSrs, M.G. Schmidt, Eur. Phys. J. C 6 (1999) 175 [hep-th/9803144].
139. H. T. Sato and M. G. Schmidt, Nucl. Phys. B 560, 551 (1999) [hep-th/9812229]
140. H. T. Sato, M. G. Schmidt and C. Zahlten, Nucl. Phys. B 579, 492 (2000) [hepth/0003070]
141. B. Kors and M. G. Schmidt, Two-loop Feynman diagrams in Yang-Mills theory from bosonic string amplitudes, hep-th/0003171.
142. S. M. Kuzenko and I. N. McArthur, JHEP 0310, 029 (2003) [hep-th/0308136]; Relaxed super self-duality and effective action, hep-th/0403082; Relaxed super selfduality andj\f=4 SYM at two loops, hep-th/0403240].
143. R. J. Crewther, Phys. Rev. Lett. 28, 1421 (1972).
144. M. S. Chanowitz and J. R. Ellis, Phys. Lett. B 40, 397 (1972).
145. S. L. Adler, J. C. Collins and A. Duncan, Phys. Rev. D 15, 1712 (1977).
146. J. C. Collins, A. Duncan and S. D. Joglekar, Phys. Rev. D 16, 438 (1977).
147. H. Pagels and E. Tomboulis, Nucl. Phys. B 143, 485 (1978).
148. K. Fujikawa, Phys. Rev. D 48, 3922 (1993).
149. J. Grundberg and T. H. Hansson, Annals Phys. 242, 413 (1995) [hep-th/9407139].
150. M. A. Shifman and A. I. Vainshtein, Sov. J. Nucl. Phys. 44, 321 (1986) [Yad. Piz. 44, 498 (1986)].
151. J. P. Bornsen and A. E. van de Ven, Nucl. Phys. B 657, 257 (2003) [hep-th/0211246].
152. M. E. Peskin and D. V. Schroeder, An Introduction To Quantum Field Theory, (Addison-Wesley, Reading, 1995).
153. S. G. Gorishnii, A. L. Kataev, S. A. Larin and L. R. Surguladze, Phys. Lett. B 256, 81 (1991).
154. R. Jost and J. M. Luttinger, Helv. Phys. Acta 23 (1950), 201.
155. J. Rosner, Phys. Rev. Lett. 17, 1190 (1966); Ann. Phys. 44, 11 (1967).
156. E. de Rafael and J. Rosner, Ann. Phys. 82, 369 (1974).
157. S. G. Gorishnii, A. L. Kataev and S. A. Larin, Phys. Lett. B 194, 429 (1987).
158. T. van Ritbergen, J. A. M. Vermaseren and S. A. Larin, Phys. Lett. B 400, 379 (1997) [hep-ph/9701390]
159. J. A. M. Vermaseren, S. A. Larin and T. van Ritbergen, Phys. Lett. B 405, 327 (1997) [hep-ph/9703284].
160. C. M. Bender, R. W. Keener and R. E. Zippel, Phys. Rev. D 15, 1572 (1977).
161. D. J. Broadhurst, R. Delbourgo and D. Kreimer, Phys. Lett. B 366, 421 (1996) [hepph/9509296]
162. D. J. Broadhurst, Phys. Lett. B 466, 319 (1999) [hep-ph/9909336]; Dimensionally continued multi-loop gauge theory, hep-th/9909185].
163. G. V. Dunne, H. Gies and C. Schubert, JHEP 0211, 032 (2002) [hep-th/0210240].
164. G. V. Dunne and C. Schubert, Phys. Lett. B 526, 55 (2002) [hep-th/0111134].
165. G. V. Dunne and C. Schubert, JHEP 0208, 053 (2002) [hep-th/0205004].
166. G. V. Dunne and C. Schubert, JHEP 0206, 042 (2002) [hep-th/0205005].
167. R. Gastmans and T. T. Wu, The ubiquitous photon: helicity method for QED and QCD, (Oxford University Press, New York, 1990).
168. M. L. Mangano and S. J. Parke, Phys. Rept. 200, 301 (1991).
169. Z. Bern, G. Chalmers, L. J. Dixon and D. A. Kosower, Phys. Rev. Lett. 72, 2134 (1994) [hep-ph/9312333].
170. Z. Bern and A. G. Morgan, Nucl. Phys. B 467, 479 (1996) [hep-ph/9511336].
171. G. Mahlon, Phys. Rev. D 49, 2197 (1994) [hep-ph/9311213].
172. Z. Bern, A. De Freitas and L. Dixon, JHEP 0203, 018 (2002) [hep-ph/0201161]
173. T. Binoth, E. W. N. Glover, P. Marquard and J. J. van der Bij, JHEP 0205, 060(2002) [hep-ph/0202266].
174. L. C. Martin, C. Schubert and V. M. Villanueva Sandoval, Nucl. Phys. B 668, 335 (2003) [hep-th/0301022].
175. C. Lee, H. W. Lee and P. Y. Pac, Nucl. Phys. B 201, 429 (1982).
176. E. W. Glover, Nucl. Phys. Proc. Suppl. 116, 3 (2003) [hep-ph/0211412]
177. Z. Bern, Nucl. Phys. Proc. Suppl. 117, 260 (2003) [hep-ph/0212406].
178. D. Kreimer, Adv. Theor. Math. Phys. 2, 303 (1998) [q-alg/9707029]
179. A. Connes and D. Kreimer, Commun. Math. Phys. 210, 249 (2000) [hep-th/9912092]
180. D. Kreimer, Knots and Feynman Diagrams, (Cambridge Univ Press, 2000).
181. G. V. Dunne, JHEP 0402, 013 (2004) [hep-th/0311167].
182. C. Anastasiou, Z. Bern, L. Dixon and D. A. Kosower, Phys. Rev. Lett. 91, 251602 (2003) [hep-th/0309040].
183. A. A. Vladimirov, Theor. Math. Phys. 43, 417 (1980).
184. K. G. Chetyrkin and F. V. Tkachov, Nucl. Phys. B 192, 159 (1981).