Casimir energy for a piecewise uniform string

I. Brevik and H. B. Nielsen
Phys. Rev. D 41, 1185 – Published 15 February 1990
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Abstract

The Casimir energy for the transverse oscillations of a piecewise uniform closed string is calculated. The string consists of two parts I and II, endowed in general with different tensions and mass densities, although adjusted in such a way that the velocity of sound always equals the velocity of light. The dispersion equation is worked out under general conditions and the frequency spectrum is determined in special cases. When the ratio LII/LI between the string lengths is an integer, it is in principle possible to determine the frequency spectrum through solving algebraic equations of increasingly high degree. The Casimir energy relative to the uniform string is in general found to be negative, although in the special case LI=LII the energy is equal to zero. Delicate points in the regularization procedure are discussed; in particular, it turns out that a straightforward use of the Riemann ζ-function regularization method leads to an incorrect expression for the Casimir energy.

  • Received 31 July 1989

DOI:https://doi.org/10.1103/PhysRevD.41.1185

©1990 American Physical Society

Authors & Affiliations

I. Brevik

  • Division of Applied Mechanics, University of Trondheim-Norges Tekniske H?gskole, N-7034 Trondheim, Norway

H. B. Nielsen

  • The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen O?, Denmark

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Issue

Vol. 41, Iss. 4 — 15 February 1990

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