Systematics of the relationship between vacuum energy calculations and heat-kernel coefficients

Journal of Physics A: Mathematical and General

Volumn 36, Issue 24, 2003, Pages 6857-6873

  Fulling, S A ^a,b  

^a TEXAS A AND M UNIVERSITY   (United States)

^b MATHEMATICAL SCIENCES RESEARCH INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038200771     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/36/24/320     Document Type: Article

References (47)

1. Beneventano C G and Santangelo E M 1996 Connection between ζ and cutoff regularizations of Casimir energies Int. J. Mod. Phys. A 11 2871-86
2. Bernasconi F, Graf G M and Hasler D 2003 The heat kernel expansion for the electromagnetic field in a cavity Preprint math-ph/0302035
3. Birrell N D and Davies P C W 1982 Quantum Fields in Curved Space (Cambridge: Cambridge University Press)
4. Blau S K, Visser M and Wipf A 1988 Zeta functions and the Casimir energy Nucl. Phys. B 310 163-80
5. Bressi G, Carugno G, Onofrio R and Ruoso G 2002 Measurement of the Casimir force between parallel metallic surfaces Phys. Rev. Lett. 88 041804
6. Bunch T S, Christensen S M and Fulling S A 1978 Massive quantum field theory in two-dimensional Robertson-Walker spacetime Phys. Rev. D 18 4435-59
7. Candelas P 1982 Vacuum polarization in the presence of dielectric and conducting surfaces Ann. Phys., NY 143 241-95
8. Candelas P 1986 Vacuum energy in the bag model Ann. Phys., NY 167 257-84
9. Chan H B, Aksyuk V A, Kleiman R N, Bishop D J and Capasso F 2001 Quantum mechanical actuation of microelectromechanical systems by the Casimir force Science 291 1941-4
10. Chen G and Zhou J 1992 Boundary Element Methods (London: Academic)
11. Cognola G, Vanzo L and Zerbini S 1992 Regularization dependence of vacuum energy in arbitrarily shaped cavities J. Math. Phys. 33 222-8
12. Deutsch D and Candelas P 1979 Boundary effects in quantum field theory Phys. Rev. D 20 3063-80
13. Estrada R 1998 The Cesàro behaviour of distributions Proc. R. Soc. A 454 2425-43
14. Estrada R and Fulling S A 1999 Distributional asymptotic expansions of spectral functions and of the associated Green kernels Electron. J. Differ. Equ. 1999 No. 7
15. Estrada R, Gracia-Bondía J M and Várilly J C 1998 On summability of distributions and spectral geometry Commun. Math. Phys. 191 219-48
16. Ford L H and Svaiter N F 1998 Vacuum energy density near fluctuating boundaries Phys. Rev. D 58 065007
17. Fulling S A 1999 What we should have learned from G H Hardy about quantum field theory under external conditions The Casimir Effect Fifty Years Later ed M Bordag (Singapore: World Scientific) pp 145-54
18. Fulling S A 2002 Periodic orbits, spectral oscillations, scaling, and vacuum energy: beyond HaMiDeW Nucl. Phys. B (Proc. Suppl.) 104 161-4
19. Fulling S A, Gorbar E V and Romero C T 2000 Spectral Riesz-Cesaro means: how the square root function helps us to see around the world Electron. J. Differ. Equ. Conf 04 87-101
20. Fulling S A and Gustafson R A 1999 Some properties of Riesz means and spectral expansions Electron. J. Differ. Equ. 1999 No. 6
21. Gilkey P B 1980 The spectral geometry of the higher order Laplacian Duke Math. J. 47 511-28
22. Gilkey P B and Grubb G 1998 Logarithmic terms in asymptotic expansions of heat operator traces Commun. Partial Differ. Equ. 23 777-92
23. Graham N, Jaffe R L, Khemani V, Quandt M, Scandurra M and Weigel H 2002 Calculating vacuum energies in renormalizable quantum field theories: a new approach to the Casimir problem Nucl. Phys. B 645 49-84
24. Graham N, Jaffe R L, Khemani V, Quandt M, Scandurra M and Weigel H 2002 Casimir energies in light of quantum field theory Preprint hep-th/0207205
25. Graham N, Jaffe R L and Weigel H 2002 Casimir effects in renormalizable quantum field theories Int. J. Mod. Phys. A 17 846-69
26. Graham N and Olum K D 2002 Negative energy densities in quantum field theory with a background potential Preprint hep-th/0211244
27. Hardy G H 1916 The second theorem of consistency for summable series Proc. London Math. Soc. 15 72-88
28. Hörmander L 1969 On the Riesz means of spectral functions and eigenfunction expansions for elliptic differential operators Belfer Graduate School of Science Annual Science Conf. Proc. Some Recent Advances in the Basic Sciences vol 2 (1965-66) ed A Gelbart (New York: Yeshiva University) pp 155-202
29. Hörmander L 1968 The spectral function of an elliptic operator Acta Math. 121 193-218
30. Kay B S 1979 Casimir effect in quantum field theory Phys. Rev. D 20 3052-62
31. Kennedy G, Critchley R and Dowker J S 1980 Finite temperature field theory with boundaries: stress tensor and surface action renormalization Ann. Phys., NY 125 346-400
32. Kirsten K 2002 Spectral Functions in Mathematics and Physics (Boca Raton, FL: CRC)
33. Lamoreaux S K 1997 Demonstration of the Casimir force in the 0.6 to 6 μm range Phys. Rev. Lett. 78 5-8
34. Milton K A 1980 Semiclassical electron models: Casimir self-stress in dielectric and conducting balls Ann. Phys., NY 127 49-61
35. Milton K A 2001 The Casimir Effect: Physical Manifestations of Zero-Point Energy (Singapore: World Scientific)
36. Milton K A 2002 Calculating Casimir energies in renormalizable quantum field theory Preprint hep-th/0210081
37. Milton K A, DeRaad L L and Schwinger J 1978 Casimir self-stress on a perfectly conducting spherical shell Ann. Phys., NY 115 388-403
38. Mohideen U and Roy A 1998 Precision measurement of the Casimir force from 0.1 to 0.9 μm Phys. Rev. Lett. 81 4549-52
39. Olum K D and Graham N 2002 Static negative energies near a domain wall Preprint gr-qc/0205134
40. Parentani R 1993 The energy-momentum tensor in Fulling-Rindler vacuum Class. Quantum Grav. 10 1409-15
41. Romeo A and Saharian A A 2002 Casimir effect for scalar fields under Robin boundary conditions on plates J. Phys. A 35 1297-320
42. Roy A and Mohideen U 1999 Demonstration of the nontrivial boundary dependence of the Casimir force Phys. Rev. Lett. 82 4380-3
43. Santangelo E M 2002 Evaluation of Casimir energies through spectral functions Theor. Math. Phys. 131 527-42 [Teor Mat. Fiz. 131 98-117]; the preprint version, hep-th/0104025, is recommended, as the published English version has suffered from reverse translation
44. Santangelo E M 2002 Evaluation of Casimir energies through spectral functions Theor. Math. Phys. 131 527-42 [Teor Mat. Fiz. 131 98-117]; the preprint version, hep-th/0104025, is recommended, as the published English version has suffered from reverse translation
45. Svaiter B F and Svaiter N F 1993 Zero point energy and analytic regularizations Phys. Rev. D 47 4581-5
46. Svaiter N F and Svaiter B F 1991 Casimir effect in a D-dimensional flat spacetime and the cut-off method J. Math. Phys. 32 175-80
47. Svaiter N F and Svaiter B F 1992 The analytic regularization zeta function method and the cut-off method in the Casimir effect J. Phys. A 25 979-89