Casimir Theory of the Relativistic Piecewise Uniform String

Details Casimir Theory of the Relativistic Piecewise Uniform String Casimir Theory of the Relativistic Piecewise Uniform String

1998-11-25

arxiv.org/abs/hep-th/9811219v1

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, latex, no figures. Talk given at the conference "Quantum Field Theory Under the Influence of External Conditions", L

Scientific paper

The Casimir energy for the transverse oscillations of a piecewise uniform closed string is calculated. The string is relativistic in the sense that the velocity of transverse waves is always equal to c. The great adaptibility of this string model with respect to various regularization methods is pointed out. We survey several regularization methods: the cutoff method, the complex contour integration method, and the zeta-function method. The most powerful method in the present case is the contour integration method. The Casimir energy turns out to be negative, and the more so the larger is the number of pieces in the string. The thermodynamic free energy F is calculated for a two-piece string in the limit when the tension ratio x = T_I/T_II approaches zero. For large values of the length ratio s = L_II/L_I, the Hagedorn temperature becomes proportional to the square root of s.

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