Note on the point-splitting procedure to evaluate vacuum fluctuation in certain cylindrically symmetric backgrounds

I. Brevik; G. E. A. Matsas; E. S. Moreira, Jr

doi:10.1103/PhysRevD.58.027502

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Note on the point-splitting procedure to evaluate vacuum fluctuation in certain cylindrically symmetric backgrounds

I. Brevik^*

G. E. A. Matsas^† and E. S. Moreira, Jr.^‡

Department of Applied Mechanics, Norwegian University of Science and Technology, N-7034 Trondheim, Norway

Instituto de Física Teórica, Universidade Estadual Paulista, Rua Pamplona 145, 01405-900, São Paulo, São Paulo, Brazil

^*Email address: Iver.H.Brevik@mtf.ntnu.no
^†Email address: matsas@axp.ift.unesp.br
^‡Email address: moreira@axp.ift.unesp.br

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Phys. Rev. D 58, 027502 – Published 23 June, 1998

DOI: https://doi.org/10.1103/PhysRevD.58.027502

Abstract

We reexamine the two-point function approaches used to study vacuum fluctuation in wedge-shaped regions and conical backgrounds. The appearance of divergent integrals is discussed and circumvented. The issue is considered in the context of a massless scalar field in cosmic string spacetime.

References (13)

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N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, England, 1982).
S. A. Fulling, Aspects of Quantum Field Theory in Curved Space-time (Cambridge University Press, Cambridge, England, 1989).
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I. Brevik and M. Lygren, Ann. Phys. (N.Y.) 251, 157 (1996).
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E. S. Moreira, Jr., Nucl. Phys. B451, 365 (1995).
V. P. Frolov and E. M. Serebriany, Phys. Rev. D 35, 3779 (1987); ibid.B. Linet, 35, 536 (1987); Class. Quantum Grav. 9, 2429 (1992); J. S. Dowker, Phys. Rev. D 36, 3095 (1987); ibid.36, 3742 (1987); A. G. Smith, in The Formation and Evolution of Cosmic Strings, Proceedings of the Cambridge Workshop, Cambridge, England, 1989, edited by G. W. Gibbons, S. W. Hawking, and T. Vachaspati (Cambridge University Press, Cambridge, England, 1990); G. E. A. Matsas, Phys. Rev. D 44, 2593 (1991); V. B. Bezerra, J. Math. Phys. 38, 2553 (1997).
I. S. Gradshteyn and I. W. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980).
E. S. Moreira, Jr., Ph.D. thesis, University of London, 1997.

[c1] H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948).

[c2] N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, England, 1982).

[c3] S. A. Fulling, Aspects of Quantum Field Theory in Curved Space-time (Cambridge University Press, Cambridge, England, 1989).

[c4] D. G. Boulware, Phys. Rev. D 11, 1404 (1975).

[c5] D. Deutsch and P. Candelas, Phys. Rev. D 20, 3063 (1979).

[c6] T. M. Helliwell and D. A. Konkowski, Phys. Rev. D 34, 1918 (1986).

[c7] G. E. A. Matsas, Phys. Rev. D 41, 3846 (1990).

[c8] I. Brevik and M. Lygren, Ann. Phys. (N.Y.) 251, 157 (1996).

[c9] A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series (Gordon and Breach, Amsterdam, 1986), Vol. 2.

[c10] E. S. Moreira, Jr., Nucl. Phys. B451, 365 (1995).

[c11] V. P. Frolov and E. M. Serebriany, Phys. Rev. D 35, 3779 (1987); ibid.B. Linet, 35, 536 (1987); Class. Quantum Grav. 9, 2429 (1992); J. S. Dowker, Phys. Rev. D 36, 3095 (1987); ibid.36, 3742 (1987); A. G. Smith, in The Formation and Evolution of Cosmic Strings, Proceedings of the Cambridge Workshop, Cambridge, England, 1989, edited by G. W. Gibbons, S. W. Hawking, and T. Vachaspati (Cambridge University Press, Cambridge, England, 1990); G. E. A. Matsas, Phys. Rev. D 44, 2593 (1991); V. B. Bezerra, J. Math. Phys. 38, 2553 (1997).

[c12] I. S. Gradshteyn and I. W. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980).

[c13] E. S. Moreira, Jr., Ph.D. thesis, University of London, 1997.

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Note on the point-splitting procedure to evaluate vacuum fluctuation in certain cylindrically symmetric backgrounds

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