Self-consistent solution for the polarized vacuum in a no-photon QED model

Journal of Physics A: Mathematical and General

Volumn 38, Issue 20, 2005, Pages 4483-4499

  Hainzl, Christian ^a,b   Lewin, Mathieu ^a   Séré, Eric ^a  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

^b UNIVERSITÉ PARIS SUD   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 18744362441     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/38/20/014     Document Type: Article

References (57)

1. Abrikosov A A, Halatnikov I and Landau L D 1956 On the quantum theory of fields Nuovo Cim. Suppl. 3 80-104 (reprinted in 1965 Collected Papers of L. D. Landau ed D Ter Haar (Oxford: Pergamon))
2. Aste A, Baur G, Hencken K, Trautmann D and Scharf G 2002 Electron-positron pair production in the external electromagnetic field of colliding relativistic heavy ions Eur. Phys. J. C 23 545-50
3. Bach V 1992 Error bound for the Hartree-Fock energy of atoms and molecules Commun. Math. Phys. 147 527-48
4. Bach V, Barbaroux J-M, Helffer B and Siedentop H 1999 On the stability of the relativistic electron-positron field Commun. Math. Phys. 201 445-60
5. Bach V, Lieb E H and Solovej J P 1994 Generalized Hartree-Fock theory and the Hubbard model J. Stat. Phys. 76 3-89
6. Borie E and Rinker G A 1982 Rev. Mod. Phys. 54 67
7. Chaix P and Iracane D 1989 From quantum electrodynamics to mean field theory: I. The Bogoliubov-Dirac-Fock formalism J. Phys. B: At. Mol. Opt. Phys. 22 3791-814
8. Chaix P, Iracane D and Lions P L 1989 From quantum electrodynamics to mean field theory: II. Variational stability of the vacuum of quantum electrodynamics in the mean-field approximation J. Phys. B: At. Mol. Opt. Phys. 22 3815-28
9. Chaix P 1990 Une Méthode de Champ Moyen Relativiste et Application à l'Etude du Vide de l'Electrodynamique Quantique PhD Thesis University Paris VI
10. Dirac P-A-M 1934 Théorie du positron Solvay Report (Paris: Gauthier-Villars) XXV, 353 S pp 203-12 (reprinted in 1958 Selected Papers on Quantum Electrodynamics ed J Schwinger (New York: Dover))
11. Dirac P A M 1934 Discussion of the infinite distribution of electrons in the theory of the positron Proc. Camb. Philos. Soc. 30 150-63
12. Dyson F J 1949 The S matrix in quantum electrodynamics Phys. Rev. 75 1736-55
13. Esteban M J and Séré E 1999 Solutions of the Dirac-Fock equations for atoms and molecules. Commun. Math. Phys. 203 499-530
14. Esteban M J and Séré E 2001 Nonrelativistic limit of the Dirac-Fock equations Ann. Henri Poincaré 2 941-61
15. Esteban M J and Séré E 2002 A max-min principle for the ground state of the Dirac-Fock functional Contemp. Math. 307 135-9
16. Foldy L L and Eriksen E 1954 Some physical consequences of vacuum polarization Phys. Rev. 95 1048-51
17. Furry W H 1937 A symmetry theorem in the positron theory Phys. Rev. 51 125
18. Furry W H 1951 On bound states and scattering in positron theory Phys. Rev. 81 115-24
19. Furry W H and Oppenheimer J R 1934 On the theory of the electron and positive Phys. Rev. II Ser. 45 245-62
20. Fierz H and Scharf G 1979 Particle interpretation for external field problems in QED Helv. Phys. Acta 52 437-53
21. Glauber R, Rarita W and Schwed P 1960 Vacuum polarization effects on energy levels in μ-mesonic atoms Phys. Rev. 120 609-13
22. Greiner W, Müller B and Rafelski J 1985 Quantum Electrodynamics of Strong Fields Texts and Monographs in Physics 1st edn (Berlin: Springer)
23. Hamm A and Schütte D 1990 How to remove divergences from the QED-Hartree approximation J. Phys. A. Math. Gen. 23 3969-82
24. Hainzl C 2004 On the vacuum polarization density caused by an external field Ann. Henri Poincaré 5 1137-57
25. Hainzl C, Lewin M and Séré E Existence of a stable polarized vacuum in the Bogoliubov-Dirac-Fock approximation Commun. Math. Phys. at press
26. Hainzl C and Siedentop H 2003 Non-Perturbative mass and charge renormalization in relativistic no-photon quantum electrodynamics Commun. Math. Phys. 243 241-60
27. Heisenberg W 1934 Bemerkungen zur Diracschen Theorie des Positrons Z. Phys. 90 209-31
28. Itzykson C and Zuber J-B 1980 Quantum Field Theory (New York: McGraw-Hill)
29. Kato T 1966 Perturbation theory for linear operators Grundlehren der mathematischen Wissenschaften vol 132 1st edn (Berlin: Springer)
30. Klaus M and Scharf G 1977 The regular external field problem in quantum electrodynamics Helv. Phys. Acta 50 779-802
31. Klaus M and Scharf G 1977 Vacuum polarization in fock space Helv. Phys. Acta 50 803-14
32. Landau L D 1955 On the quantum theory of fields Bohr Volume (Oxford: Pergamon) (reprinted in 1965 Collected Papers of L D Landau ed D Ter Haar (Oxford: Pergamon))
33. Landau L D and Pomeranchuk I 1955 On point interactions in quantum electro dynamics Dokl. Akad. Nauk SSSR 102 489-92 (reprinted in 1965 Collected Papers of L D Landau ed D Ter Haar (Oxford: Pergamon))
34. Landau L D 1960 Fundamental problems Pauli Memorial Volume (New York: Interscience) p 245 (reprinted in 1965 Collected Papers of L D Landau ed D Ter Haar (Oxford: Pergamon))
35. Lieb E H 1981 Variational principle for many-fermion systems Phys. Rev. Lett. 46 457-9
36. Lieb E H and Siedentop H 2000 Renormalization of the regularized relativistic electron-positron field Commun. Math. Phys. 213 673-83
37. Mohr P J, Plunien G and Soff G 1998 QED corrections in heavy atoms Phys. Rep. 293 227-369
38. Paturel E 2000 Solutions of the Dirac-Fock equations without projector Ann. Henri Poincaré 1 1123-57
39. Pauli W and Rose M E 1936 Remarks on the polarization effects in the positron theory Phys. Rev. II 49 462-5
40. Pomeranchuk I Ya, Sudakov V V and Ter-Martirosyan K A 1956 Vanishing of renormalized charges in field theories with point interaction Phys. Rev. 103 784-802
41. Reinhard P-G, Greiner W and Arenhvel H 1971 Electrons in strong external fields Nucl. Phys. A 166 173-97
42. Reinhardt J, Müller B and Greiner W 1981 Theory of positron production in heavy-ion collision Phys. Rev. A 24 103-28
43. Ruijsenaars S N M 1977 On Bogoliubov transformations for systems of relativistic charged particles J. Math. Phys. 18 517-26
44. Scharf G and Seipp H P 1982 Charged vacuum, spontaneous positron production and all that Phys. Lett. B 108 196-8
45. Schwinger J 1949 Quantum electrodynamics II. vacuum polarization and self-energy Phys. Rev. II Ser. 75 651-79
46. Schwinger J 1951 On the green's function of quantized fields: II. Proc. Natl. Acad. Sci. 37 455-9
47. Seipp H P 1982 On the S-operator for the external field problem of QED Helv. Phys. Acta 55 1-28
48. Serber R 1935 Linear modifications in the Maxwell field equations Phys. Rev. II Ser. 48 49-54
49. Shabaev V M 2002 Two-time green's function method in quantum electrodynamics of high-z few-electron atoms Phys. Rep. 356 119-228
50. Shale D and Stinespring W F 1965 Spinor representations of infinite orthogonal groups J. Math. Mech. 14 315-22
51. Simon B 1979 Trace Ideals and their Applications (London Mathematical Society Lecture Notes Series vol 35) (Cambridge: Cambridge University Press)
52. Soff G and Mohr P 1988 Phys. Rev. A 38 5066
53. Solovej J P 1994 Proof of the ionization conjecture in a reduced Hartree-Fock model Invent. Math. 104 291-311
54. Swirles B 1935 The relativistic self-consistent field Proc. R. Soc. A 152 625-49
55. Thaller B 1992 The Dirac Equation (Berlin: Springer)
56. Uehling E A 1935 Polarization effects in the positron theory Phys. Rev. II Ser. 48 55-63
57. Weisskopf V 1936 Über die elektrodynamik des vakuums auf grund der quantentheorie des elektrons Math.-Fys. Medd., Danske Vid. Selsk. 16 1-39 (reprinted in 1958 Selected Papers on Quantum Electrodynamics ed J Schwinger (New York: Dover))