Local and global casimir energies: Divergences, renormalization, and the coupling to gravity

Lecture Notes in Physics

Volumn 834, Issue , 2011, Pages 39-95

  Milton, Kimball A ^a  

^a UNIVERSITY OF OKLAHOMA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79960649313     PISSN: 00758450     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-642-20288-9_3     Document Type: Conference Paper

References (116)

1. Casimir, H.B.G.: On the attraction between two perfectly conducting plates. Proc. Kon. Ned. Akad. Wetensch. 51, 793 (1948)
2. London, F.: Theory and system of molecular forces. Z. Physik 63, 245 (1930)
3. Casimir, H.B.G., Polder, D.: The influence of retardation on the London-Van Der Waals forces. Phys. Rev. 73, 360 (1948)
4. Casimir, H.B.G.: In: Bordag, M. (ed.) The Casimir Effect 50 Years Later: The Proceedings of the Fourth Workshop on Quantum Field Theory Under the Influence of External Conditions, World Scientific, Singapore, p. 3, (1999)
5. Jaffe, R.L.: Unnatural acts: Unphysical consequences ofimposing boundary conditions on quantum fields. AIP Conf. Proc. 687, p. 3 (2003). arXiv:hep-th/0307014
6. Lifshitz, E.M.: Zh. Eksp. Teor. Fiz. 29, 94 (1956), [English translation: The theory of molecular attractive forces between solids. Soviet Phys. JETP 2,73 (1956)]
7. Dzyaloshinskii, I.D., Lifshitz, E. M., Pitaevskii, L.P.: Zh. Eksp. Teor. Fiz. 37, 229 (1959), [English translation: Van der Waals forces in liquid films. Soviet Phys. JETP 10, 161 (1960)]
8. Dzyaloshinskii, I.D., Lifshitz, E.M., Pitaevskii, L.P., Usp. Fiz. Nauk 73, 381(1961), [English translation: General theory of van der Waals forces. Soviet Phys. Usp. 4, 153 (1961)]
9. Bordag, M., Klimchitskaya, G.L., Mohideen, U., Mostepanenko, V.M.: Advances in the Casimir Effect. Int. Ser. Monogr. Phys. 145,1 (2009). (Oxford University Press, Oxford, 2009)
10. Klimchitskaya, G.L., Mohideen, U., Mostepanenko, V.M.: The Casimir force between real materials: experiment and theory. Rev. Mod. Phys. 81, 1827 (2009). arXiv:0902.4022[cond-mat.other]
11. Deryagin(Derjaguin), B.V.: Analysis of friction and adhesion IV: The theory of the adhesion of small particles. Kolloid Z. 69, 155 (1934)
12. Deryagin(Derjaguin), B.V. et al.: Effect of contact deformations on the adhesion of particles. J. Colloid. Interface Sci. 53, 314 (1975)
13. Blocki, J., Randrup, J., Swiatecki, W. J., Tsang, C.F.: Proximity forces. Ann. Phys. (N.Y.) 105, 427 (1977)
14. Milton, K.A.: Recent developments in the Casimir effect. J. Phys. Conf. Ser. 161, 012001 (2009). [hep-th]]
15. Boyer, T.H.: Quantum electromagnetic zero point energy of a conducting spherical shell and the Casimir model for a charged particle. Phys. Rev. 174, 1764 (1968)
16. Lukosz, W.: Electromagnetic zero-point energy and radiation pressure for a rectangular cavity. Physica 56, 109 (1971)
17. Lukosz, W.: Electromagnetic zero-point energy shift induced by conducting closed surfaces. Z. Phys. 258, 99 (1973)
18. Lukosz, W.: Electromagnetic zero-point energy shift induced by conducting surfaces. II. The infinite wedge and the rectangular cavity. Z. Phys. 262, 327 (1973)
19. Ambjørn, J., Wolfram, S.: Properties of the vacuum. I. Mechanical and thermodynamic. Ann. Phys. (N.Y.) 147, 1 (1983)
20. Balian, R., Duplantier, B.: Electromagnetic waves near perfect conductors. II. Casimir effect. Ann. Phys. (N.Y.) 112, 165 (1978)
21. Bernasconi, F., Graf, G.M., Hasler, D.: The heat kernel expansion for the electromagnetic field in a cavity. Ann. Henri Poincaré 4, 1001 (2003). arXiv:math-ph/0302035
22. Fulling, S.A., Milton, K.A., Parashar, P., Romeo, A., Shajesh, K.V., Wagner, J.: How does Casimir energy fall?. Phys. Rev. D 76, 025004 (2007). arXiv:hep-th/0702091
23. Milton, K.A., Parashar, P., Shajesh, K.V., Wagner, J.: How does Casimir energy fall? II. Gravitational acceleration of quantum vacuum energy. J. Phys. A 40, 10935 (2007). [hep-th]]
24. Milton, K.A., Wagner, J.: Exact Casimir Interaction Between Semitransparent Spheres and Cylinders. Phys. Rev. D 77, 045005 (2008). [arXiv:0711.0774 [hep-th]]
25. Milton, K.A., Wagner, J.: Multiple Scattering Methods in Casimir Calculations. J. Phys. A 41, 155402 (2008). [hep-th]]
26. Wagner, J., Milton, K.A., Parashar, P.: Weak Coupling Casimir Energies for Finite Plate Configurations. J. Phys. Conf. Ser. 161, 012022 (2009). [arXiv:0811.2442 [hep-th]]
27. DeRaad, L.L. Jr., Milton, K.A.: Casimir Selfstress On A Perfectly Conducting Cylindrical Shell. Ann. Phys. (N.Y.) 136, 229 (1981)
28. Bender, C.M., Milton, K.A.: Casimir effect for a D-dimensional sphere. Phys. Rev. D 50, 6547 (1994). arXiv:hep-th/9406048
29. Gosdzinsky, P., Romeo, A.: Energy of the vacuum with a perfectly conducting and infinite cylindrical surface. Phys. Lett. B 441, 265 (1998). arXiv:hep-th/9809199
30. Brevik, I., Marachevsky, V.N., Milton, K.A.: Identity of the van der Waals force and the Casimir effect and the irrelevance of these phenomena to sonoluminescence. Phys. Rev. Lett. 82, 3948 (1999). arXiv:hep-th/9810062
31. Cavero-Peláez, I., Milton, K.A.: Casimir energy for a dielectric cylinder. Ann. Phys. (N.Y.) 320, 108 (2005). arXiv:hep-th/0412135
32. Klich, I.: Casimir's energy of a conducting sphere and of a dilute dielectric ball. Phys. Rev. D 61, 025004 (2000). arXiv:hep-th/9908101
33. Milton, K.A., Nesterenko, A.V., Nesterenko, V.V.: Mode-by-mode summation for the zero point electromagnetic energy of an infinite cylinder. Phys. Rev. D 59, 105009 (1999)
34. Kitson, A.R., Signal, A.I.: Zero-point energy in spheroidal geometries. J. Phys. A 39, 6473 (2006). arXiv:hep-th/0511048
35. Kitson, A.R., Romeo, A.: Perturbative zero-point energy for a cylinder ofelliptical section. Phys. Rev. D 74, 085024 (2006). arXiv:hep-th/0607206
36. Milton, K.A.: Calculating Casimir energies in renormalizable quantum field theory. Phys. Rev. D 68, 065020 (2003). arXiv:hep-th/0210081.
37. Cavero-Peláez, I., Milton, K.A., Kirsten, K.: Local and global Casimir energies for a semitransparent cylindrical shell. J. Phys. A 40, 3607 (2007). arXiv:hep-th/0607154
38. Milton, K.A.: The Casimir Effect: Physical Manifestations of Zero-Point Energy. World Scientific, Singapore (2001)
39. Bordag, M., Hennig, D., Robaschik, D.: Vacuum energy in quantum field theory with external potentials concentrated on planes. J. Phys. A 25, 4483 (1992)
40. Bordag, M., Kirsten, K., Vassilevich, D.: Ground state energy for a penetrable sphere and for a dielectric ball. Phys. Rev. D 59, 085011 (1999). arXiv:hep-th/9811015
41. Graham, N., Jaffe, R.L., Weigel, H.: Casimir effects in renormalizable quantum field theories. Int. J. Mod. Phys. A 17, 846 (2002). arXiv:hep-th/0201148
42. Graham, N., Jaffe, R.L., Khemani, V., Quandt, M., Scandurra, M., Weigel, H.: Calculating vacuum energies in renormalizable quantum field theories: a new approach to the Casimir problem. Nucl. Phys. B 645, 49 (2002). arXiv:hep-th/0207120
43. Graham, N., Jaffe, R.L., Khemani, V., Quandt, M., Scandurra, M., Weigel, H.: Casimir energies in light of quantum field theory. Phys. Lett. B 572, 196 (2003). arXiv:hep-th/ 0207205
44. Graham, N., Jaffe, R.L., Khemani, V., Quandt, M., Scandurra, M., Weigel, H.: The Dirichlet Casimir problem. Nucl. Phys. B 677, 379 (2004). arXiv:hep-th/0309130
45. Milton, K.A.: Casimir energies and pressures for delta-function potentials. J. Phys. A 37, 6391 (2004). arXiv:hep-th/0401090
46. Milton, K.A.: The Casimir effect: Recent controversies and progress. J. Phys. A 37, R209 (2004). arXiv:hep-th/0406024
47. Kantowski, R., Milton, K.A.: Scalar Casimir energies in M4 × S . Phys. Rev. D 35, 549 (1987)
48. Brevik, I., Jensen, B., Milton, K.A.: Comment on ''Casimir energy for spherical boundaries''. Phys. Rev. D 64, 088701 (2001). arXiv:hep-th/0004041
49. Weigel H.: Dirichlet spheres in continuum quantum field theory. In: Milton, K.A. (ed.) Proceedings of the 6th Workshop on Quantum Field Theory Under the Influence of External Conditions, p. 195, (Rinton Press, Princeton, N.J., 2004) arXiv:hep-th/0310301
50. Fulling, S.A.: Systematics of the relationship between vacuum energy calculations and heat kernel coefficients. J. Phys. A 36, 6857 (2003)
51. Graham, N., Olum, K.D.: Negative energy densities in quantum field theory with a background potential. Phys. Rev. D 67, 085014 (2003). arXiv:quant-ph/0302117
52. Callan, C.G. Jr., Coleman, S., Jackiw, R.: A new improved energy-momentum tensor. Ann. Phys. (N.Y.) 59, 42 (1970)
53. Olum, K.D., Graham, N.: Static negative energies near a domain wall. Phys. Lett. B 554, 175 (2003). arXiv:gr-qc/0205134
54. Romeo, A., Saharian, A.A.: Casimir effect for scalar fields under Robin boundary conditions on plates. J. Phys. A 35, 1297 (2002). arXiv:hep-th/0007242
55. Romeo, A., Saharian, A.A.: Vacuum densities and zero-point energy for fields obeying Robin conditions on cylindrical surfaces. Phys. Rev. D 63, 105019 (2001). arXiv:hepth/ 0101155
56. Saharian, A.A.: Scalar Casimir effect for D-dimensional spherically symmetric Robin boundaries. Phys. Rev. D 6, 125007 (2001). arXiv:hep-th/0012185
57. Saharian, A.A.: On the energy-momentum tensor for a scalar field on manifolds with boundaries. Phys. Rev. D 69, 085005 (2004). arXiv:hep-th/0308108
58. Brown, L.S., Maclay, GJ.: Vacuum stress between conducting plates: An Image solution. Phys. Rev. 184, 1272 (1969)
59. Actor, A.A., Bender, I.: Boundaries immersed in a scalar quantum field. Fortsch. Phys. 44, 281 (1996)
60. Dowker, J.S., Kennedy, G.: Finite temperature and boundary effects in static space-times. J. Phys. A 11, 895 (1978)
61. Deutsch, D., Candelas, P.: Boundary effects in quantum field theory. Phys. Rev. D 20, 3063 (1979)
62. Brevik, I., Lygren, M.: Casimir effect for a perfectly conducting wedge. Ann. Phys. (N.Y.) 251, 157 (1996)
63. Sopova, V., Ford, L.H.: The electromagnetic field stress tensor near dielectric half-spaces. In: Milton, K.A. (ed.) Proceedings of the 6th Workshop on Quantum Field Theory Under the Influence of External Conditions, p.140. Rinton Press, Princeton, NJ, (2004)
64. Sopova, V., Ford, L.H.: The Electromagnetic Field Stress Tensor between Dielectric Half-Spaces. Phys. Rev. D 72, 033001 (2005). arXiv:quant-ph/0504143
65. Graham, N.: Do casimir energies obey general relativity energy conditions?. In: Milton, K.A. (ed.) Proceedings of the 6th Workshop on Quantum Field Theory Under the Influence of External Conditions, Rinton Press, Princeton, NJ (2004)
66. Graham, N., Olum, K.D.: Plate with a hole obeys the averaged null energy condition. Phys. Rev. D 72, 025013 (2005). arXiv:hep-th/0506136
67. Milton, K.A.: Semiclassical electron models: Casimir self-stress in dielectric and conducting balls. Ann. Phys. (N.Y.) 127, 49 (1980)
68. Milton, K.A., DeRaad, L.L. Jr., Schwinger, J.: Casimir self-stress on aperfectly conducting spherical shell. Ann. Phys. (N.Y.) 115, 388 (1978)
69. Candelas, P.: Vacuum energy in the presence of dielectric and conducting surfaces. Ann. Phys. (N.Y.) 143, 241 (1982)
70. Candelas, P.: Vacuum energy in the bag model. Ann. Phys. (N.Y.) 167, 257 (1986)
71. Bordag, M., Mohideen, U., Mostepanenko, V.M.: New developments in the Casimir effect. Phys. Rept. 353, 1 (2001). arXiv:quant-ph/0106045
72. Sen, S.: Geometrical determination of the sign of the Casimir force in two spatial dimensions. Phys. Rev. D 24, 869 (1981)
73. Sen, S.: A calculation of the Casimir force on a circular boundary. J. Math. Phys. 22, 2968 (1981)
74. Cavero-Peláez, I., Milton, K.A., Wagner, J.: Local casimir energies for a thin spherical shell. Phys. Rev. D 73, 085004 (2006). arXiv:hep-th/0508001
75. Barton, G.: Casimir energies of spherical plasma shells. J. Phys. A 37, 1011 (2004)
76. Scandurra, M.: The ground state energy of a massive scalar field in the background of a semi-transparent spherical shell. J. Phys. A 32, 5679 (1999). arXiv:hep-th/9811164
77. Bender, C.M., Milton, K.A.: Scalar Casimir effect for a D-dimensional sphere. Phys. Rev. D 50, 6547 (1994). arXiv:hep-th/9406048
78. Leseduarte, S., Romeo, A.: Complete zeta-function approach to the electromagnetic Casimir effect for a sphere. Europhys. Lett. 34, 79 (1996)
79. Leseduarte, S., Romeo, A.: Complete zeta-function approach to the electromagnetic Casimir effect for spheres and circles. Ann. Phys. (N.Y.) 250, 448 (1996). arXiv:hepth/9605022
80. Klich, I.: Casimir energy of a conducting sphere and of a dilute dielectric ball. Phys. Rev. D 61, 025004 (2000). arXiv:hep-th/9908101
81. Bordag, M., Vassilevich, D.V.: Nonsmooth backgrounds in quantum field theory. Phys. Rev. D 70, 045003 (2004). arXiv:hep-th/0404069
82. Milton, K.A.: Zero-point energy in bag models. Phys. Rev. D 22, 1441 (1980)
83. Milton, K.A.: Zero-point energy of confined fermions. Phys. Rev. D 22, 1444 (1980)
84. Milton, K.A.: Vector Casimir effect for a D-dimensional sphere. Phys. Rev. D 55, 4940 (1997). arXiv:hep-th/9611078
85. Leseduarte, S., Romeo, A.: Influence ofamagnetic fluxon on the vacuum energy of quantum fields confined by a bag. Commun. Math. Phys. 193, 317 (1998). arXiv:hep-th/9612116
86. Davies, B.: Quantum electromagnetic zero-point energy of a conducting spherical shell. J. Math. Phys. 13, 1324 (1972)
87. Schwartz-Perlov, D., Olum, K.D.: Energy conditions for a generally coupled scalar field outside a reflecting sphere. Phys. Rev. D 72, 065013 (2005). arXiv:hep-th/0507013
88. Scandurra, M.: Vacuum energy of a massive scalar field in the presence of a semi-transparent cylinder. J. Phys. A 33, 5707 (2000). arXiv:hep-th/0004051
89. Gilkey, P.B., Kirsten, K., Vassilevich, D.V.: Heat trace asymptotics with transmittal boundary conditions and quantum brane-world scenario. Nucl. Phys. B 601, 125 (2001)
90. Nesterenko, V.V., Pirozhenko, I.G.: Spectral zeta functions for a cyllinder and a circle. J. Math. Phys. 41, 4521 (2000)
91. Kennedy, G., Critchley, R., Dowker, J.S.: Finite temperature field theory with bound-aries: stress tensor and surface action renormalization. Ann. Phys. (N.Y.) 125, 346 (1980)
92. Romeo, A., Saharian, A.A.: Casimir effect for scalar fields under Robin boundary conditions on plates. J. Phys. A 35, 1297 (2002). arXiv:hep-th/0007242
93. Fulling, S.A., Kaplan, L., Kirsten, K., Liu, Z.H., Milton, K.A.: Vacuum stress and closed paths in rectangles, pistons, and pistols. J. Phys. A 42, 155402 (2009). arXiv:0806. 2468[hep-th]
94. Born, M.: The theory of the rigid electron in the kinematics of the relativity principle. Ann. Phys. (Leipzig) 30, 1 (1909)
95. Calloni, E., Di Fiore, L., Esposito, G., Milano, L., Rosa, L.: Vacuum fluctuation force on a rigid Casimir cavity in a gravitational field. Phys. Lett. A 297, 328 (2002)
96. Karim, M., Bokhari, A.H., Ahmedov, BJ.: The Casimir force in the Schwarzchild metric. Class. Quant. Grav. 17, 2459 (2000)
97. Caldwell, R.R.: Gravitation of the Casimir effect and the cosmological non-constant. arXiv:astro-ph/0209312
98. Sorge, F.: Casimir effect in a weak gravitational field. Class. Quant. Grav. 22, 5109 (2005)
99. Bimonte, G., Calloni, E., Esposito, G., Rosa, L.: Energy-momentum tensor for a Casimir apparatus in a weak gravitational field. Phys. Rev. D 74, 085011 (2006)
100. Bimonte, G., Esposito, G., Rosa, L.: From Rindler space to the electromagnetic energy-momentum tensor of a Casimir apparatus in a weak gravitational field. Phys. Rev. D 78, 024010 (2008). arXiv:0804.2839 [hep-th]
101. Saharian, A.A., Davtyan, R.S., Yeranyan, A.H.: Casimir energy in the Fulling-Rindler vacuum. Phys. Rev. D 69, 085002 (2004). arXiv:hep-th/0307163
102. Jaekel. M.T., Reynaud, S.: Mass, inertia and gravitation. arXiv:0812.3936 [gr-qc]
103. Estrada, R., Fulling, S.A., Liu, Z., Kaplan, L., Kirsten, K., Milton, K.A.: Vacuum stress-energy density and its gravitational implications. J. Phys. A 41, 164055 (2008)
104. Actor, A.A.: Scalar quantum fields confined by rectangular boundaries. Fortsch. Phys. 43, 141 (1995)
105. Schaden, M.: Semiclassical electromagnetic Casimir self-energies. arXiv:hep-th/0604119
106. Gies, H., Klingmuller, K.: Casimir edge effects. Phys. Rev. Lett. 97, 220405 (2006). arXiv:quant-ph/0606235
107. Gies, H., Klingmuller, K.: Worldline algorithms for Casimir configurations Phys. Rev. D 74, 045002 (2006). arXiv:quant-ph/0605141
108. Gies, H., Klingmuller, K.: Casimir effect for curved geometries: PFA validity limits. Phys. Rev. Lett. 96, 220401 (2006). arXiv:quant-ph/0601094
109. Jaffe, R.L., Scardicchio, A.: The casimir effect and geometric optics. Phys. Rev. Lett. 92, 070402 (2004). arXiv:quant-ph/0310194
110. Scardicchio, A., Jaffe, R.L.: Casimir effects: an optical approach I. foundations and examples. Nucl. Phys. B 704, 552 (2005). arXiv:quant-ph/0406041
111. Schroeder, O., Scardicchio, A., Jaffe, R.L.: The Casimir energy for a hyperboloid facing a plate in the optical approximation. Phys. Rev. A 72, 012105 (2005). arXiv:hep-th/0412263
112. Graham, N., Shpunt, A., Emig, T., Rahi, S.J., Jaffe, R.L., Kardar, M.: Casimir force at a knife's edge. Phys. Rev. D 81, 061701 (2010). arXiv:0910.4649 [quant-ph]
113. Rahi, S.J., Rodriguez, A.W., Emig, T., Jaffe, R.L., Johnson, S.G., Kardar, M.: Nonmonotonic effects of parallel sidewalls on Casimir forces between cylinders. Phys. Rev. A 77, 030101 (2008). arXiv:0711.1987 [cond-mat.stat-mech]
114. Farhi, E., Graham, N., Haagensen, P., Jaffe, R.L.: Finite quantum fluctuations about static field configurations. Phys. Lett. B 427, 334 (1998). arXiv:hep-th/9802015
115. Graham, N., Jaffe, R.L.: Energy, central charge, and the BPS bound for 1+1 dimensional supersymmetric solitons. Nucl. Phys. B 544, 432 (1999). arXiv:hep-th/9808140
116. Cavero-Peláez, I., Guilarte, J.M.: Local analysis of the sine-Gordon kink quantum fluctuations. to appear In: Milton, K. A., Bordag, M. (eds.) Proceedings of the 9th Conference on Quantum Field Theory Under the Influence of External Conditions, World Scientific, Singapore (2010). arXiv:0911.4450 [hep-th]