Quantum effective actions from nonperturbative worldline dynamics

Journal of High Energy Physics

Volumn , Issue 8, 2005, Pages 1719-1753

  Gies, Holger ^a   Sanchez Guillen, Joaquin ^b   Vázquez, Ricardo A ^b  

^a INSTITUT FÜR THEORETISCHE PHYSIK   (Germany)

^b UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

Nonperturbative Effects

Indexed keywords

EID: 24944527763     PISSN: 10298479     EISSN: None     Source Type: Journal    
DOI: 10.1088/1126-6708/2005/08/067     Document Type: Article

References (61)

1. W. Heisenberg and H. Euler, Consequences of Dirac's theory of positrons 1936 Z. Phys. 98 714
2. V. Weisskopf, Über die Elektrodynamik des Vakuums auf Grund der Quantentheorie des Elektrons 1936 K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 14 1
3. S.R. Coleman and E. Weinberg, Radiative corrections as the origin of spontaneous symmetry breaking 1973 Phys. Rev. D 7 1888
4. R.P. Feynman, Mathematical formulation of the quantum theory of electromagnetic interaction 1950 Phys. Rev. 80 440
5. , An operator calculus having applications in quantum electrodynamics 1951 Phys. Rev. 84 108
6. M.B. Halpern and W. Siegel, The particle limit of field theory: a new strong coupling expansion 1977 Phys. Rev. D 16 2486
7. M.B. Halpern, A. Jevicki and P. Senjanovic, Field theories in terms of particle-string variables: spin, internal symmetries and arbitrary dimension 1977 Phys. Rev. D 16 2476
8. A.M. Polyakov, Gauge fields and strings Harwood, Chur 1987
9. Z. Bern and D.A. Kosower, Color decomposition of one loop amplitudes in gauge theories 1991 Nucl. Phys. B 362 389
10. Z. Bern and D.A. Kosower, The computation of loop amplitudes in gauge theories 1992 Nucl. Phys. B 379 451
11. M.J. Strassler, Field theory without Feynman diagrams: one loop effective actions 1992 Nucl. Phys. B 385 145 [hep-ph/9205205]
12. M.G. Schmidt and C. Schubert, On the calculation of effective actions by string methods 1993 Phys. Lett. B 318 438 [hep-th/9309055]
13. M. Reuter, M.G. Schmidt and C. Schubert, Constant external fields in gauge theory and the spin 0, 1/2, 1 path integrals 1997 Ann. Phys. (NY) 259 313 [hep-th/9610191]
14. R. Shaisultanov, On the string-inspired approach to QED in external field 1996 Phys. Lett. B 378 354 [hep-th/9512142]
15. For a review, see C. Schubert, C. Schubert, Perturbative quantum field theory in the string-inspired formalism 2001 Phys. Rep. 355 73 [hep-th/0101036]
16. Z. Bern, D.C. Dunbar and T. Shimada, String based methods in perturbative gravity 1993 Phys. Lett. B 312 277 [hep-th/9307001]
17. D.C. Dunbar and P.S. Norridge, Calculation of graviton scattering amplitudes using string based methods 1995 Nucl. Phys. B 433 181 [hep-th/9408014]
18. D. Cangemi, E. D'Hoker and G.V. Dunne, Derivative expansion of the effective action and vacuum instability for qed in (2+1)-dimensions 1995 Phys. Rev. D 51 2513 [hep-th/9409113]
19. F.A. Dilkes and D.G.C. McKeon, Off-diagonal elements of the dewitt expansion from the quantum mechanical path integral 1996 Phys. Rev. D 53 4388 [hep-th/9509005]
20. S.L. Adler and C. Schubert, Photon splitting in a strong magnetic field: recalculation and comparison with previous calculations 1996 Phys. Rev. Lett. 77 1695 [hep-th/9605035]
21. V.P. Gusynin and I.A. Shovkovy, Derivative expansion for the one-loop effective lagrangian in qed 1996 Can. J. Phys. 74 282-289 [hep-ph/9509383]
22. V.P. Gusynin and I.A. Shovkovy, Derivative expansion of the effective action for qed in 2+1 and 3+1 dimensions 1999 J. Math. Phys. 40 5406 [hep-th/9804143]
23. C.D. Fosco, J. Sanchez-Guillen and R.A. Vazquez, Some results on Migdal's particle path-integral representation for the Dirac propagator 2004 Phys. Rev. D 69 105022 [hep-th/0310191]
24. F. Bastianelli and C. Schubert, One loop photon graviton mixing in an electromagnetic field, I 2005 J. High Energy Phys. JHEP02(2005)069 [gr-qc/0412095]
25. L. Magnea, R. Russo and S. Sciuto, Two-loop Euler-Heisenberg effective actions from charged open strings [hep-th/0412087]
26. F. Brummer, M.G. Schmidt and Z. Tavartkiladze, Worldlines on orbifolds and the Fayet-Iliopoulos term 2005 Eur. Phys. J. C 41 393 [hep-th/0412284]
27. H. Gies and K. Langfeld, Quantum diffusion of magnetic fields in a numerical worldline approach 2001 Nucl. Phys. B 613 353 [hep-ph/0102185]
28. H. Gies and K. Langfeld, Loops and loop clouds: a numerical approach to the worldline formalism in qed 2002 Int. J. Mod. Phys. A 17 966 [hep-ph/0112198]
29. M.G. Schmidt and I.-O. Stamatescu, Determinant calculations using random walk worldline loops 2003 Nucl. Phys. (Proc. Suppl.) 119 1030 [hep-lat/0209120]
30. M.G. Schmidt and I. Stamatescu, Matter determinants in background fields using random walk world line loops on the lattice 2003 Mod. Phys. Lett. A 18 1499
31. K. Langfeld, L. Moyaerts and H. Gies, Fermion-induced quantum action of vortex systems 2002 Nucl. Phys. B 646 158 [hep-th/0205304]
32. H. Gies, K. Langfeld and L. Moyaerts, Casimir effect on the worldline 2003 J. High Energy Phys. JHEP06(2003)018 [hep-th/0303264]
33. L. Moyaerts, K. Langfeld and H. Gies, Worldline approach to the Casimir effect [hep-th/0311168]
34. G.C. Wick, Properties of Bethe-Salpeter wave functions 1954 Phys. Rev. 96 1124
35. R.E. Cutkosky, Solutions of a Bethe-Salpeter equations 1954 Phys. Rev. 96 1135
36. I.K. Affleck, O. Alvarez and N.S. Manton, Pair production at strong coupling in weak external fields 1982 Nucl. Phys. B 197 509
37. R. Rosenfelder and A.W. Schreiber, Polaron variational methods in the particle representation of field theory, 1. General formalism 1996 Phys. Rev. D 53 3337 [nucl-th/9504002]
38. C. Alexandrou, R. Rosenfelder and A.W. Schreiber, Worldline path integral for the massive dirac propagator: a four-dimensional approach 1999 Phys. Rev. A 59 1762 [hep-th/9809101]
39. C. Alexandrou, R. Rosenfelder and A.W. Schreiber, Non-perturbative mass renormalization in quenched QED from the worldline variational approach 2000 Phys. Rev. D 62 085009 [hep-th/0003253]
40. J. Sanchez-Guillen and R.A. Vazquez, Non-perturbative quenched propagator beyond the infrared approximation 2002 Phys. Rev. D 65 105001 [hep-th/0201065]
41. Y.A. Simonov and J.A. Tjon, The Feynman-Schwinger representation for the relativistic two particle amplitude in field theory 1993 Ann. Phys. (NY) 228 1
42. T. Nieuwenhuis and J.A. Tjon, Bound state solutions of scalar qed in (2+1)-dimensions for zero photon mass 1995 Phys. Lett. B 355 283 [hep-ph/9506346]
43. 2 chi theory 1996 Phys. Rev. Lett. 77 814 [hep-ph/9606403]
44. C. Savkli, J. Tjon and F. Gross, Feynman-schwinger representation approach to nonperturbative physics 1999 Phys. Rev. D 60 055210 [hep-ph/9906211]
45. C. Savkli, J. Tjon and F. Gross, erratum 2000 Phys. Rev. C 61 069901
46. C. Savkli, F. Gross and J. Tjon, Nonperturbative dynamics of scalar field theories through the feynman-schwinger representation 2005 Phys. Atom. Nucl. 68 842 [nucl-th/0404068]
47. N. Brambilla and A. Vairo, From the feynman-schwinger representation to the non-perturbative relativistic bound state interaction 1997 Phys. Rev. D 56 1445 [hep-ph/9703378]
48. Y.A. Simonov and J.A. Tjon, The feynman-schwinger representation in QCD 2002 Ann. Phys. (NY) 300 54 [hep-ph/0205165]
49. L. Alvarez-Gaumé, Supersymmetry and the Atiyah-Singer index theorem 1983 Comm. Math. Phys. 90 161
50. C.M. Bender, K.A. Milton and V.M. Savage, Solution of Schwinger-Dyson equations for PT-symmetric quantum field theory 2000 Phys. Rev. D 62 085001 [hep-th/9907045]
51. H. Gies and J. Hammerling, Geometry of spin-field coupling on the worldline [hep-th/0505072]
52. C. Fosco, J.S. Sánchez-Guillén and R.A. Vázquez, in preparation (2005)
53. D. Fliegner, P. Haberl, M.G. Schmidt and C. Schubert, The higher derivative expansion of the effective action by the string inspired method, II 1998 Ann. Phys. (NY) 264 51 [hep-th/9707189]
54. S.L. Lebedev and V.I. Ritus, Virial representation of the imaginary part of the lagrange function of the electromagnetic field 1984 Zh. Eksp. Teor. Fiz. 86 408
55. G.V. Dunne and C. Schubert, Multiloop information from the QED effective lagrangian [hep-th/0409021]
56. M. Gockeler et al., Is there a Landau pole problem in QED? 1998 Phys. Rev. Lett. 80 4119 [hep-th/9712244]
57. H. Gies and J. Jaeckel, Renormalization flow of qed 2004 Phys. Rev. Lett. 93 110405 [hep-ph/0405183]
58. C. Itzykson and J.B. Zuber, Quantum field theory Mc Graw Hill, New York 1980
59. S.K. Kauffmann and J. Rafelski, Analytic study of a sequence of path integral approximations for simple quantum systems at low temperature 1984 Z. Physik C 24 157
60. J. Glimm and A.M. Jaffe, Quantum physics. A functional integral point of view Springer, New York 1981
61. F. David and K.J. Wiese, Instanton calculus for the self-avoiding manifold model [cond-mat/0409765]