Multidimensional cut-off technique, odd-dimensional Epstein zeta functions and Casimir energy of massless scalar fields

Journal of Physics A: Mathematical and General

Volumn 39, Issue 3, 2006, Pages 685-712

  Edery, Ariel ^a  

^a BISHOP'S UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 29244476098     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/39/3/017     Document Type: Article

References (77)

1. Casimir H G 1948 Proc. Kon. Neth. Akad. Wet. 51 793
2. Sparnaay M J 1958 Physica 24 751
3. Lamoreaux S K 1997 Phys. Rev. Lett. 78 5
4. Mohideen U and Roy A 1998 Phys. Rev. Lett. 81 4549
5. Klimchiskaya G L, Roy A, Mohideen U and Mostepanenko V M 1999 Phys. Rev. A 60 3487
6. Roy A and Mohideen U 1999 Phys. Rev. Lett. 82 4380
7. Roy A, Lin C-Y and Mohideen U 1999 Phys. Rev. D 60 111101 (R)
8. Harris B W, Chen F and Mohideen U 2000 Phys. Rev. A 62 052109
9. Chen F, Klimchitskaya G L, Mohideen U and Mostepanenko V M 2004 Phys. Rev. A 69 022117
10. Ederth T 2000 Phys. Rev. A 62 062104
11. Bressi G, Carugno G, Onofrio R and Ruoso G 2002 Phys. Rev. Lett. 88 041804
12. Chen F, Mohideen U, Klimchitskaya G L and Mostepanenko V M 2002 Phys. Rev. Lett. 88 101801
13. Chen F, Mohideen U, Klimchitskaya G L and Mostepanenko V M 2002 Phys. Rev. A 66 032113
14. Decca R S, López D, Fischbach E and Krause D E 2003 Phys. Rev. Lett. 91 050402
15. Hamed N, Dimopoulos S and Dvali G 1998 Phys. Lett. B 429 263
16. Klimchitskaya G L, Decca R S, Fischbach E, Krause D E, López D and Mostepanenko V M 2005 Int. J. Mod. Phys. A 20 2205-21
17. Marciak-Kozlowska J and Kozlowski M 2005 Preprint cond-mat/0506226
18. Chan H B, Aksyuk V A, Kleiman R N, Bishop D J and Capasso F 2001 Science 291 1941
19. Chan H B, Aksyuk V A, Kleiman R N, Bishop D J and Capasso F 2001 Phys. Rev. Lett. 87 211801
20. Roberts D C and Pomeau Y 2005 Phys. Rev. Lett. 95 145303
21. Roberts D C and Pomeau Y 2005 Preprint cond-mat/0503757
22. Pitaevskii L and Stringari S 1999 Phys. Rev. Lett. 81 4541
23. Stampur Kurn D M et al 1999 Phys. Rev. Lett. 83 2876
24. Greiner M et al 2002 Nature 415 39
25. Polchinski J 1998 String Theory, Vol I: An Introduction to the Bosonic String (Cambridge: Cambridge University Press)
26. Zee A 2003 Quantum Field Theory in a Nutshell (Princeton, NJ: Princeton University Press)
27. Itzykson C and Zuber J B 1980 Quantum Field Theory (New York: McGraw-Hill)
28. Guth A Relativistic quantum field theory: I. Spring 2003 http://ocw.mit.edu/OcwWeb/Physics/8-323Relativistic-Quantum-Field-Theory- ISpring2003
29. Vogels J M, Xu K and Ketterle W 2002 Phys. Rev. Lett. 89 020401
30. Roberts D C, Gasenzer T and Burnett K 2002 J. Phys. B 35 L113-8
31. Pu H and Meystre P 2000 Phys. Rev. Lett. 85 3987
32. Duran L M et al 2000 Phys. Rev. Lett. 85 3991
33. Milton K A 2001 The Casimir Effect (Singapore: World Scientific)
34. Mostepanenko V M and Trunov N N 1997 The Casimir Effect and Its Applications (Oxford: Oxford University Press)
35. Mlton K A 2004 J. Phys. A: Math. Gen. 37 209
36. Bordag M, Mohideen U and Mostapanenko V M 2001 Phys. Rep. 353 1
37. Barton G 2004 Advances in Atomic and Molecular Physics (suppl. 2) ed P R Berman (New York: Academic)
38. Jaeckel M and Reynaud S 1997 Rep. Prog. Phys. 60 863
39. Visser M 1998 Class. Quantum Gravity 15 1767
40. Barceló C, Liberati S and Visser M 2001 Class. Quantum Gravity 18 1137
41. Svaiter N F and Svaiter B F 1991 J. Math. Phys. 32 1
42. Svaiter N F and Svaiter B F 1992 J. Phys. A: Math. Gen. 25 979
43. Lukosz W 1973 Z. Phys. 262 327
44. Mamayev S G and Trunov N N 1979 Theor. Math. Phys. 38
45. Mostepanenko V M and Trunov N N 1988 Sov. Phys.-Usp. 31
46. Beneventano C G and Santagelo E M 1996 Int. J. Mod. Phys. A 11 2871
47. Ambjørn J and Wolfram S 1983 Ann. Phys., NY 147 1
48. Caruso F, Neto P, Svaiter B F and Svaiter N F 1991 Phys. Rev. D 43 1300
49. Cheng H, Li X, Li J and Zhai X 1997 Phys. Rev. D 56 2155
50. Maclay G 2000 Phys. Rev. A 61 052110
51. Elizalde E 1998 Commun. Math. Phys. 198 83
52. Lee T D, Huang K and Yang C N 1957 Phys. Rev. 106 1135
53. Bogoliubov N 1947 J. Phys. 11 23
54. Hardy G H and Wright E M 1979 An Introduction to the Theory of Numbers 5th edn (Oxford: Clarendon)
55. Shimura G 2002 Am. J. Math. 124 1059
56. Arfken G B and Weber H J 1995 Mathematical Methods for Physicists 4th edn (New York: Academic)
57. Gradshteyn I S and Ryzhik I M 2000 Table of Integrals, Series and Products 4th edn (New York: Academic)
58. Edery A 2003 J. Math. Phys. 44 599
59. Edery A 2004 Preprint math-ph/0411056
60. Kirsten K 2001 Spectral Functions in Mathematics and Physics (London/Boca Raton, FL: Chapman and Hall/CRC)
61. Elizalde E 1995 Ten Physical Applications of Spectral Zeta Functions (Berlin: Springer)
62. Elizalde E, Odintsov S D, Romeo A, Bytsenko A A and Zerbini S 1994 Zeta Regularization Techniques with Applications (Singapore: World Scientific)
63. Esposito G, Fucci G, Kamenshchik A Y and Kirsten K 2005 Class. Quantum Gravity 22 957
64. Cognola G, Elizalde E and Zerbini S 2004 Phys. Lett. B 585 155
65. Elizalde E, Nojiri S, Odintsov S and Ogushi S 2003 Phys. Rev. D 67 063515
66. Fulling S 2003 J. Phys. A: Math. Gen. 36 6857
67. Elizade E 2001 J. Phys. A: Math. Gen. 34 3025
68. Esposito G, Gilkey P and Kirsten K 2005 J. Phys. A: Math. Gen. 38 2259
69. Schakel A 2003 J. Phys. Stud. 7 140
70. Li X, Shi X and Zhang J 1991 Phys. Rev. D 44 560
71. Ortenzi G and Speafico M 2004 J. Phys. A: Math. Gen. 37 11499
72. Elizalde E and Romeo A 1989 J. Math. Phys. 30 1133
73. Elizalde E 1989 J. Phys. A: Math. Gen. 22 931
74. Elizalde E 1989 J. Phys. A: Math. Gen. 22 931
75. Cognola G, Vanzo L and Zerbini S 1992 J. Math. Phys. 33 222
76. Kirsten K 1992 J. Phys. A: Math. Gen. 25 6297
77. Weisstein E Sum of squares function MathWorld-A Wolfram Web Resource.http://mathworld.wolfram.com/SumofSquaresFunction.html