On the Casimir energy for a 2N-piece relativistic string

Details On the Casimir energy for a 2N-piece relativistic string On the Casimir energy for a 2N-piece relativistic string

1997-03-26

arxiv.org/abs/hep-th/9703187v1

J.Math.Phys.38:2774-2785,1997

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, LaTeX. To appear in J. Math. Physics, June 1997

Scientific paper

10.1063/1.532018

The Casimir energy for the transverse oscillations of a piecewise uniform closed string is calculated. The string consists of 2N pieces of equal length, of alternating type I and type II material, and is taken to be relativistic in the sense that the velocity of sound always equals the velocity of light. By means of a new recursion formula we manage to calculate the Casimir energy for arbitrary integers N. Agreement with results obtained in earlier works on the string is found in all special cases. As basic regularization method we use the contour integration method. As a check, agreement is found with results obtained from the \zeta function method (the Hurwitz function) in the case of low N (N = 1-4). The Casimir energy is generally negative, and the more so the larger is the value of N. We illustrate the results graphically in some cases. The generalization to finite temperature theory is also given.

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