Bethe-Salpeter approach for relativistic positronium in a strong magnetic field

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 73, Issue 12, 2006, Pages

  Shabad, A E ^a   Usov, V V ^b  

^a LEBEDEV PHYSICAL INSTITUTE   (Russian Federation)

^b WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33745514419     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.73.125021     Document Type: Article

References (71)

1. R. Loudon, Am. J. Phys. 27, 649 (1959); AJPIAS 0002-9505 10.1119/1.1934950
2. R.J. Elliot and R. Loudon, J. Phys. Chem. Solids 8, 382 (1959); JPCSAW 0022-3697 10.1016/0022-3697(59)90371-3
3. R.J. Elliot R. Loudon J. Phys. Chem. Solids 15, 196 (1960). JPCSAW 0022-3697 10.1016/0022-3697(60)90243-2
4. M.A. Ruderman, Phys. Rev. Lett. 27, 1306 (1971); PRLTAO 0031-9007 10.1103/PhysRevLett.27.1306
5. D. Lai, Rev. Mod. Phys. 73, 629 (2001). RMPHAT 0034-6861 10.1103/RevModPhys.73.629
6. P.A. Sturrock, Astrophys. J. 164, 529 (1971); ASJOAB 0004-637X 10.1086/150865
7. M.A. Ruderman and P.G. Sutherland, Astrophys. J. 196, 51 (1975); ASJOAB 0004-637X 10.1086/153393
8. D. Eichler, M. Livio, T. Piran, and D. Schramm, Nature (London) 340, 126 (1989); NATUAS 0028-0836 10.1038/340126a0
9. T.R. White and A.P. Lightman, Astrophys. J. 340, 1024 (1989); ASJOAB 0004-637X 10.1086/167455
10. V.V. Usov and D.B. Melrose, Aust. J. Phys. AUJPAS 0004-9506 48, 571 (1995);
11. C. Thompson and R.C. Duncan, Mon. Not. R. Astron. Soc. 275, 255 (1995); MNRAA4 0035-8711
12. V.V. Usov, Phys. Rev. Lett. 80, 230 (1998); PRLTAO 0031-9007 10.1103/PhysRevLett.80.230
13. M.G. Baring and A.K. Harding, Astrophys. J. 547, 929 (2001). ASJOAB 0004-637X 10.1086/318390
14. R.N. Manchester, G.B. Hobbs, A. Teoh, and M. Hobbs, Astron. J. 129, 1993 (2005). ANJOAA 0004-6256 10.1086/428488
15. F.C. Michel, Theory of Neutron Star Magnetospheres (University of Chicago Press, Chicago, 1991).
16. A.E. Shabad and V.V. Usov, Astrophys. Space Sci. 117, 309 (1985); APSSBE 0004-640X 10.1007/BF00650157
17. H. Herold, H. Ruder, and G. Wunner, Phys. Rev. Lett. 54, 1452 (1985); PRLTAO 0031-9007 10.1103/PhysRevLett.54.1452
18. V.V. Usov and D.B. Melrose, Astrophys. J. 464, 306 (1996). ASJOAB 0004-637X 10.1086/177321
19. E. Witten, Nucl. Phys. NUPBBO 0550-3213 B249, 557 (1985); 10.1016/0550-3213(85)90022-7
20. E.M. Chudnovsky, G.B. Field, D.N. Spergel, and A. Vilenkin, Phys. Rev. D PRVDAQ 0556-2821 34, 944 (1986). 10.1103/PhysRevD.34.944
21. V. Berezinsky, B. Hnatyk, and A. Vilenkin, Phys. Rev. D 64, 043004 (2001). PRVDAQ 0556-2821 10.1103/PhysRevD.64.043004
22. L.B. Leinson and V.N. Oraevskii, Sov. J. Nucl. Phys. 42, 245 (1985); SJNCAS 0038-5506
23. L.B. Leinson V.N. Oraevskii Phys. Lett. B 165, 422 (1985). PYLBAJ 0370-2693 10.1016/0370-2693(85)91258-4
24. A.E. Shabad and V.V. Usov, Astrophys. Space Sci. 128, 377 (1986). APSSBE 0004-640X 10.1007/BF00644586
25. L.B. Leinson and A. Pérez, J. High Energy Phys. JHEPFG 1029-8479 11 (2000) 039. 10.1088/1126-6708/2000/11/039
26. A.E. Shabad and V.V. Usov, Phys. Rev. Lett. 96, 180401 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.96.180401
27. L.D. Landau and E.M. Lifshits, Quantum Mechanics (Pergamon Press, Oxford, 1991).
28. In this point the situation is different from the no-magnetic-field case, where the falling to the center holds for nonphysical values of the fine structure constant, exceeding a positive critical value, αcr 1, and gives rise to the Goldstein solution [J.S. Goldstein, Phys. Rev. 91, 1516 (1953)] of the Bethe-Salpeter equations, which also corresponds to the shrinking of the energy gap between electrons and positrons. See the review articles and our recent publication. PHRVAO 0031-899X 10.1103/PhysRev.91.1516
29. Yu.M. Loskutov and V.V. Skobelev, Phys. Lett. A 56, 151 (1976). PYLAAG 0375-9601 10.1016/0375-9601(76)90626-5
30. S.S. Schweber, An Introduction to Relativistic Quantum Field Theory (Row, Peterson and Co., Evanston, IL and Elmsford, NY, 1961).
31. V.I. Ritus, Zh. Eksp. Teor. Fiz. 75, 1560 (1978) ZETFA7 0044-4510
32. [V.I. Ritus Sov. Phys. JETP SPHJAR 0038-5646 48, 778 (1978)];
33. V.I. Ritus Trudy Fiz. Inst. im. P. N. Lebedeva, Akad. Nauk. SSSR TFILAD 0203-5820 168, 52 (1986). Our definition of the matrix eigenfunctions differs from that of Ritus in that the longitudinal degrees of freedom are not included and the factor exp (ip1x1) is separated.
34. D. Lai and E.E. Salpeter, Phys. Rev. A 52, 2611 (1995). PLRAAN 1050-2947 10.1103/PhysRevA.52.2611
35. A.E. Shabad and V.V. Usov, hep-th/0512236.
36. A.E. Shabad, hep-th/0403177.
37. A.E. Shabad, J. Phys. A JPHAC5 0305-4470 38, 7419 (2005). 10.1088/0305-4470/38/33/014
38. V.P. Gusynin, V.A. Miransky, and I.A. Shovkovy, Phys. Rev. D 52, 4747 (1995); PRVDAQ 0556-2821 10.1103/PhysRevD.52.4747
39. V.P. Gusynin V.A. Miransky I.A. Shovkovy Nucl. Phys. NUPBBO 0550-3213 B462, 249 (1996); 10.1016/0550-3213(96)00021-1
40. C.N. Leung, Y.J. Ng, and A.W. Ackley, Phys. Rev. D 54, 4181 (1996). PRVDAQ 0556-2821 10.1103/PhysRevD.54.4181
41. P.I. Fomin, V.P. Gusynin, V.A. Miransky, and Yu.A. Sitenko, Riv. Nuovo Cimento RNUCAC 0035-5917 6, numero 5 (1983).
42. V.P. Gusynin, V.A. Miransky, and I.A. Shovkovy, Phys. Rev. Lett. 83, 1291 (1999); PRLTAO 0031-9007 10.1103/PhysRevLett.83.1291
43. V.P. Gusynin V.A. Miransky I.A. Shovkovy Nucl. Phys. NUPBBO 0550-3213 B563, 361 (1999); 10.1016/S0550-3213(99)00573-8
44. C.N. Leung and S.-Y. Wang, hep-ph/0510066.
45. R.C. Duncan, astro-ph/0002442.
46. I.A. Batalin and A.E. Shabad, Zh. Eksp. Teor. Fiz. 60, 894 (1971) ZETFA7 0044-4510
47. [I.A. Batalin A.E. Shabad Sov. Phys. JETP SPHJAR 0038-5646 33, 483 (1971)];
48. A.E. Shabad, Ann. Phys. (N.Y.) APNYA6 0003-4916 90, 166 (1975). 10.1016/0003-4916(75)90144-X
49. A.E. Shabad, Polarization of the Vacuum and a Quantum Relativistic Gas in an External Field (Nova Science Publishers, New York, 1991);
50. A.E. Shabad Trudy Fiz. Inst. im. P. N. Lebedeva, Akad. Nauk. SSSR TFILAD 0203-5820 192, 5 (1988).
51. A.E. Shabad, Kratkie Soobshchenia po Fizike, Sov. Phys. Lebedev Inst. Reps. 3, 13 (1976).
52. W. Dittrich and M. Reuter, Effective Lagrangians in Quantum Electrodynamics (Springer-Verlag, Berlin, 1985).
53. A. Kuznetsov and N. Mikheev, Electroweak Processes in External Electromagnetic Fields (Springer, New York, Berlin, Heidelberg, 2004).
54. A.E. Shabad, Zh. Eksp. Teor. Fiz. 125, 210 (2004) ZETFA7 0044-4510
55. [A.E. Shabad JETP 98, 186 (2004)]. Note the difference in the signs in front of k2 due to a different metric convention used here. JTPHES 1063-7761 10.1134/1.1675886
56. J.S. Heyl and L. Hernquist, J. Phys. A JPHAC5 0305-4470 30, 6485 (1997). 10.1088/0305-4470/30/18/022
57. B. Jancovici, Phys. Rev. 187, 2275 (1969); PHRVAO 0031-899X 10.1103/PhysRev.187.2275
58. R.G. Newton, Phys. Rev. 96, 523 (1954); PHRVAO 0031-899X 10.1103/PhysRev.96.523
59. R.G. Newton Phys. Rev. D 3, 626 (1971); PRVDAQ 0556-2821 10.1103/PhysRevD.3.626
60. V.N. Baier, V.M. Katkov, and V.M. Strakhovenko, Zh. Eksp. Teor. Fiz. 67, 67 (1974); ZETFA7 0044-4510
61. V.N. Baier V.M. Katkov V.M. Strakhovenko Yad. Fiz. 24, 379 (1976). IDFZA7 0044-0027
62. Yu.M. Loskutov and V.V. Skobelev, Teor. Mat. Fiz. 48, 44 (1981). TMFZAL 0564-6162
63. V.P. Gusynin and A.V. Smilga, Phys. Lett. B 450, 267 (1999). PYLBAJ 0370-2693 10.1016/S0370-2693(99)00145-8
64. A.V. Kuznetsov, N.V. Mikheev, and M.V. Osipov, Mod. Phys. Lett. A 17, 231 (2002). MPLAEQ 0217-7323 10.1142/S0217732302006321
65. Ya.B. Zel'dovich and V.S. Popov, Usp. Fiz. Nauk UFNAAG 0042-1294 105, 403 (1971)
66. [Ya.B. Zel'dovich V.S. Popov Sov. Phys. Usp. SOPUAP 0038-5670 14, 673 (1972)]. 10.1070/PU1972v014n06ABEH004735
67. W. Greiner and J. Reinhardt, Quantum Electrodynamics (Springer-Verlag, Berlin, 1992).
68. V.N. Oraevskii, A.I. Rez, and V.B. Semikoz, Zh. Eksp. Teor. Fiz. 72, 821 (1977) ZETFA7 0044-4510
69. [V.N. Oraevskii A.I. Rez V.B. Semikoz Sov. Phys. JETP SPHJAR 0038-5646 45, 428 (1977)].
70. A.E. Shabad and V.V. Usov, astro-ph/0601542.
71. N. Setô, Prog. Theor. Phys. Suppl. PTPSEP 0375-9687 95, 25 (1988).