Sign and other aspects of semiclassical Casimir energies

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 73, Issue 4, 2006, Pages

  Schaden, Martin ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CASIMIR ENERGY; MASSLESS SCALAR FIELD; SUBTRACTIONS; ZETA FUNCTION REGULARIZATION;

BOUNDARY CONDITIONS; CALCULATIONS; DEFORMATION; POLES;

QUANTUM THEORY;

EID: 33645659904     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.73.042102     Document Type: Article

References (82)

1. H. B. G. Casimir, Proc. K. Ned. Akad. Wet. PKNAAU 0370-0348 51, 793 (1948).
2. P. W. Millonni, The Quantum Vacuum (Academic, New York, 1993), especially Chaps. and.
3. V. M. Mostapanenko and N. N. Trunov, The Casimir Effect and its Applications (Clarendon, Oxford, 1997).
4. K. A. Milton, The Casimir Effect: Physical Manifestations Of Zero-Point Energy (World Scientific, River Edge, 2001).
5. D. Deutsch and P. Candelas, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.20.3063 20, 3063 (1979);
6. P. Candelas, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(82) 90029-X 143, 241 (1982);
7. P. Candelas, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(86) 90202-2 167, 257 (1986).
8. S. A. Fulling, Aspects of Quantum Field Theory in Curved Space-time (Cambridge University Press, Cambridge, 1989).
9. N. Graham, R. L. Jaffe, V. Klemani, M. Quandt, M. Scandurra, and H. Weigel, Nucl. Phys. B NUPBBO 0550-3213 10.1016/S0550-3213(02)00823-4 645, 49 (2002);
10. R. L. Jaffe, in HIGH ENERGY PHYSICS: The 25th Annual Montreal-Rochester- Syracuse-Toronto Conference on High Energy Physics, MRST 2003: A Tribute to Joe Shechter, edited by, Amir H. Fariborz, AIP Conf. Proc. No. 687 (AIP, Melville, 2003), p. 3.
11. M. Bordag, K. Kirsten, and D. Vassilevich, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.59.085011 59, 085011 (1999).
12. K. A. Milton, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.68.065020 68, 065020 (2003);
13. K. A. Milton, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/37/38/R01 37, R209 (2004).
14. S. A. Fulling, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/36/24/320 36, 6857 (2003);
15. Quantum Field Theory Under the Influence of External Conditions, edited by, K. A. Milton, (Rinton Press, Princeton, 2004).
16. H. Gies, K. Langfeld, and L. Moyaerts, J. High Energy Phys. JHEPFG 1126-6708 0306, 018 (2003).
17. T. H. Boyer, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.174.1764 174, 1764 (1968);
18. K. A. Milton, L. L. DeRaad, and J. S. Schwinger, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(78)90161-6 115, 388 (1978); Ref., and references therein.
19. F. Bernasconi, G. M. Graf, and D. Hasler, Ann. Henri Poincare AHPJFM 1424-0637 4, 1001 (2003).
20. R. Balian and B. Duplantier, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(77)90334-7 104, 300 (1977);
21. R. Balian and B. Duplantier, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(78)90083-0 112, 165 (1978);
22. Proceedings of the 15th SIGRAV Conference on General Relativity and Gravitational Physics, Villa Mondragone, Monte Porzio Catone, Italy, 2002, quant-ph/0408124.
23. M. Schaden and L. Spruch, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.935 58, 935 (1998).
24. R. L. Jaffe and A. Scardicchio, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.070402 92, 070402 (2004);
25. A. Scardicchio and R. L. Jaffe, Nucl. Phys. B NUPBBO 0550-3213 10.1016/j.nuclphysb.2004.10.017 704, 552 (2005).
26. O. Schröder, A. Scardicchio, and R. L. Jaffe, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.012105 72, 012105 (2005).
27. A. Bulgac, P. Magierski, and A. Wirzba, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.73.025007 73, 025007 (2006).
28. S. K. Lamoreaux, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 78.5 78, 5 (1997);
29. U. Mohideen and A. Roy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.4549 81, 4549 (1998);
30. T. Ederth, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.062104 62, 062104 (2000);
31. G. Bressi, G. Carugno, R. Onofrio, and G. Ruoso, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.041804 88, 041804 (2002).
32. M. C. Gutzwiller, Chaos in Classical Quantum Mechanics (Springer, Berlin, 1990) with references to the author's earlier work.
33. S. Blau, M. Visser, and A. Wipf, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(88)90059-4 310, 163 (1988).
34. K. Kirsten and E. Elizalde, Phys. Lett. B PYLBAJ 0370-2693 10.1016/0370-2693(95)01303-2 365, 72 (1996).
35. E. A. Power, Introductory Quantum Electrodynamics (Elsevier, New York, 1964), Appendix.
36. R. B. Balian and C. Bloch, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(70)90497-5 60, 401 (1970);
37. R. B. Balian and C. Bloch, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(71)90032-7 63, 592 (1971);
38. R. B. Balian and C. Bloch, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(71)90286-7 64, 271 (1971);
39. R. B. Balian and C. Bloch, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(74)90316-9 84, 559 (E) (1974);
40. R. B. Balian and C. Bloch, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(72)90006-1 69, 76 (1972);
41. R. B. Balian and C. Bloch, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(74)90421-7 85, 514 (1974).
42. W. Lukosz, Physica (Amsterdam) PHYSAG 0031-8914 10.1016/0031-8914(71) 90009-7 56, 109 (1971).
43. J. S. Dowker and R. Critchley, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/9/4/009 9, 535 (1976).
44. J. Ambjörn and S. Wolfram, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(83)90065-9 147, 1 (1983).
45. J. S. Dowker and G. Kennedy, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/11/5/020 11, 895 (1978).
46. G. Barton, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/34/19/309 34, 4083 (2001).
47. H. B. G. Casimir, Physica (Amsterdam) PHYSAG 0031-8914 19, 846 (1953).
48. P. Candelas and J. S. Dowker, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.19.2902 19, 2902 (1979).
49. S. C. Creagh, J. M. Robbins, and R. G. Littlejohn, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.42.1907 42, 1907 (1990);
50. J. M. Robbins, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/4/2/007 4, 343 (1991).
51. L. S. Brown and G. J. Maclay, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.184.1272 184, 1272 (1969).
52. B. P. Dolan and C. Nash, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF02102368 148, 139 (1992).
53. M. V. Berry and M. Tabor, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 349, 101 (1976);
54. M. V. Berry and M. Tabor, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/10/3/009 10, 371 (1977);
55. M. V. Berry and M. Tabor, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 356, 375 (1977).
56. E. B. Bogomolny, Physica D PDNPDT 0167-2789 10.1016/0167-2789(88)90075-9 31, 169 (1988).
57. P. Candelas and S. Weinberg, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(84)90001-4 237, 397 (1984);
58. D. Birmingham and S. Sen, Ann. Phys. (N.Y.) APNYA6 0003-4916 172, 451 (1986).
59. N. G. van Kampen, B. R. A. Nijboer, and K. Schramm, Phys. Lett. PYLAAG 0375-9601 10.1016/S0375-9601(99)00710-0 26A, 307 (1968).
60. J. S. Dowker, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(71) 90096-0 62, 361 (1971).
61. L. S. Schulman, Techniques and Applications of Path Integrals (Wiley, New York, 1981);
62. M. C. Gutzwiller, Phys. Scr. PHSTBO 0031-8949 T9, 184 (1985);
63. C. Grosche and F. Steiner, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(88)90297-7 182, 120 (1988).
64. E. Elizalde, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.530469 35, 3308 (1994).
65. J. B. Keller, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(58) 90032-0 4, 180 (1958);
66. in Calculus of Variations and its Applications (American Mathematical Society, Providence, 1958), p. 27;
67. J. Opt. Soc. Am. JOSAAH 0030-3941 52, 116 (1962).
68. V. P. Maslov, Théorie des Perturbations et Méthodes Asymptotiques (Dunod, Paris, 1972);
69. V. P. Maslov and M. V. Feodiriuk, Semiclassical Approximations in Quantum Mechanics (Reidel, Boston, 1981).
70. G. Kennedy and S. D. Unwin, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/13/7/007 13, L253 (1980).
71. P. Chang and J. S. Dowker, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(93)90223-C 395, 407 (1993).
72. J. S. Dowker, e-print hep-th/0510248;
73. e-print math.SP/0601334.
74. M. P. Hertzberg, R. L. Jaffe, M. Kardar, and A. Scardicchio, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.250402 95, 250402 (2005).
75. Cited in V. Hushwater, Am. J. Phys. AJPIAS 0002-9505 10.1119/1.18548 65, 381 (1997).
76. M. Schaden (in preparation).
77. F. Steiner, Phys. Lett. B PYLBAJ 0370-2693 10.1016/0370-2693(87)91646-7 188, 447 (1987).
78. J. Bolte and F. Steiner, Commun. Math. Phys. CMPHAY 0010-3616 156, 1 (1993).
79. B. S. DeWitt, Dynamical Theory of Groups and Fields (Gordon and Breach, New York, 1965).
80. T. Sakai, Tohoku Math. J. TOMJAM 0040-8735 23, 589 (1971).
81. J. Chazarain, Invent. Math. INVMBH 0020-9910 24, 65 (1974).
82. J. J. Duistermaat and V. W. Guillemin, Invent. Math. INVMBH 0020-9910 10.1007/BF01405172 29, 39 (1975), and references therein.