Abstract
We propose a subtraction-free method for calculating the quantum-field vacuum energy in the presence of nontrivial boundary conditions and logarithmically divergent terms caused by them. The method can also be used in the case where the energy levels of a system are known only numerically. Moreover, its use requires neither knowledge of the analytic form of equations for certain levels or a detailed analysis of their asymptotic behavior.
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REFERENCES
H. B. G. Casimir, Proc. K. Ned. Akad. Wetensc, 51, 793 (1948); Phys., 19, 846 (1953).
M. Bordag, U. Mohideen, and V. M. Mostepanenko, Phys.Rep., 353, 1 (2001); quant-ph/0106045 (2001).
T. H. Boyer, Phys.Rev., 174, 1764 (1968); R. Balian and R. Duplantier, Ann. Phys., 112, 165 (1978); K. A. Milton, L. L. De Raad, and J. Schwinger, Ann. Phys., 115, 388 (1978).
K. A. Milton, Phys. Rev. D, 22, 1441, 1444 (1980); G. E. Brown, A. D. Jackson, M. Rho, and V. Vento, Phys. Lett. B, 140, 285 (1984).
L. Vepstas and A. D. Jackson, Phys. Rep., 187, 109 (1990).
M. De Francia, H. Falomir, and E. M. Santangelo, Phys. Rev. D, 45, 2129 (1992); A. Hosaka and H. Toki, Phys. Rep., 277, 65 (1996).
J. Baacke and Y. Igarashi, Phys. Rev. D, 27, 460 (1983); S. K. Blau, M. Wisser, and A. Wipf, Nucl. Phys. B, 310, 163 (1988).
M. Bordag, E. Elizalde, K. Kirsten, and S. Leseduate, Phys. Rev. D, 56, 4896 (1997).
E. Elizalde, M. Bordag, and K. Kirsten, J. Phys. A, 31, 1743 (1998).
M. Bordag, B. Geyer, K. Kirsten, and E. Elizalde, Comm. Math. Phys., 179, 215 (1996).
K. A. Sveshnikov and P. K. Silaev, Theor. Math. Phys., 117, 1319 (1998); I. Yu. Malakhov, K. A. Sveshnikov, S. M. Fedorov, and M. F. Khalili, Theor. Math. Phys., 132, 1094 (2002); I. Yu. Malakhov and K. A. Sveshnikov, Theor. Math. Phys., 132, 1201 (2002).
C. Itzykson and J.-B. Zuber, Quantum Field Theory, McGraw-Hill, New York (1980).
A. O. Gel’fond, Calculus of Finite Differences [in Russian], Fizmatgiz, Moscow (1967); English transl., Hindustan Publ. Corp., Delhi, India (1971).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 143, No. 1, pp. 49–63, April, 2005.
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Malakhov, I.Y., Sveshnikov, K.A. & Silaev, P.K. Subtraction-free renormalization of the quantum-field vacuum energy in the presence of nontrivial boundary conditions. Theor Math Phys 143, 529–540 (2005). https://doi.org/10.1007/s11232-005-0088-8
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DOI: https://doi.org/10.1007/s11232-005-0088-8