Optical approach for the thermal partition function of photons

Valter Moretti; Devis Iellici

doi:10.1103/PhysRevD.55.3552

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Optical approach for the thermal partition function of photons

Valter Moretti and Devis Iellici

Dipartimento di Fisica, Università di Trento, and Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Trento, I-38 050 Povo (TN), Italy

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Phys. Rev. D 55, 3552 – Published 15 March, 1997

DOI: https://doi.org/10.1103/PhysRevD.55.3552

Abstract

The optical manifold method to compute the one-loop effective action in a static space-time is extended from the massless scalar field to the Maxwell field in any Feynman-like covariant gauge. The method is applied to the case of the Rindler space obtaining the same results as the point-splitting procedure. The result is free from Kabat’s surface terms which instead affect the $ζ$ -function or heat-kernel approaches working directly in the static manifold containing conical singularities. The relation between the optical method and the direct $ζ$ -function approach on the Euclidean Rindler manifold is discussed both in the scalar and the photon cases. Problems with the thermodynamic self-consistency of the results obtained from the stress tensor in the case of the Rindler space are pointed out.

References (33)

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[c1] D. Iellici and V. Moretti, Phys. Rev. D54, 7459 (1996).

[c2] D. Deutsch and P. Candelas, Phys. Rev. D20, 3063 (1979).

[c3] J. S. Dowker, Phys. Rev. D36, 3742 (1987).

[c4] J. S. Dowker, Class. Quantum Grav.11, L55 (1994).

[c5] S. Zerbini, G. Cognola, and L. Vanzo, Phys. Rev. D54, 2699 (1996).

[c6] V. P. Frolov and E. M. Serebriany, Phys. Rev. D35, 3779 (1987).

[c7] J. S. Dowker, Phys. Rev. D36, 3095 (1987).

[c8] G. Cognola, K. Kirsten, and L. Vanzo, Phys. Rev. D49, 1029 (1994).

[c9] D. Kabat, Nucl. Phys.B453, 281 (1995).

[c10] C. Callan and F. Wilczek, Phys. Lett. B333, 55 (1994).

[c11] G. Gibbons and M. Perry, Proc. R. Soc. London, Ser. A358, 467 (1978).

[c12] M. R. Brown and A. C. Ottewill, Phys. Rev. D31, 2514 (1985).

[c13] S. B. Giddings, Phys. Rev. D49, 4078 (1994).

[c14] J. L. F. Barbon, Phys. Rev. D50, 2712 (1994).

[c15] R. Emparan, Phys. Rev. D51, 5716 (1995).

[c16] G. Cognola, L. Vanzo, and S. Zerbini, Class. Quantum Grav.12, 1927 (1995).

[c17] J. L. F. Barbon and R. Emparan, Phys. Rev. D52, 2133 (1995).

[c18] S. P. de Alwis and N. Ohta, Phys. Rev. D52, 3529 (1995).

[c19] B. Allen, Phys. Rev. D33, 3640 (1986).

[c20] A. A. Bytsenko, G. Cognola, L. Vanzo, and S. Zerbini, Phys. Rep.266, 1 (1996).

[c21] N. D. Birrel and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, England, 1982).

[c22] F. Larsen and F. Wilczek, Nucl. Phys.B458, 249 (1996).

[c23] B. S. Kay and U. M. Studer, Commun. Math. Phys.136, 103 (1991).

[c24] G. ’t Hooft, Nucl. Phys.B256, 727 (1985).

[c25] S. N. Solodukhin, Phys. Rev. D51, 609 (1995).

[c26] D. V. Fursaev and S. N. Solodukhin, Phys. Rev. D52, 2133 (1995).

[c27] A. M. Polyakov, Phys. Lett.103B, 207 (1981).

[c28] J. S. Dowker and J. P. Schofield, Nucl. Phys.B327, 267 (1989).

[c29] N. K. Nielsen and P. van Nieuwenhuizen, Phys. Rev. D38, 3183 (1988).

[c30] R. Camporesi, Phys. Rep.196, 1 (1990).

[c31] E. Elizalde, S.D. Odintsov, A. Romeo, A.A. Bytsenko, and S. Zerbini, Zeta Regularization Techniques with Applications (World Scientific, Singapore, 1994).

[c32] I. S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980).

[c33] R. Haag, Local Quantum Physics (Springer, Berlin, 1992).

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