Thermodynamic Properties of the Relativistic Composite String - Expository Remarks

TL;DR

This paper calculates the Casimir energy and thermodynamic properties of a piecewise uniform relativistic string, exploring various regularization methods and analyzing the implications for string decay and critical temperatures.

Contribution

It provides a comprehensive analysis of the Casimir energy and thermodynamics of a relativistic composite string, highlighting the effectiveness of the contour integration method and discussing physical implications.

Findings

Casimir energy is negative and increases in magnitude with more pieces.

The contour integration method is the most effective regularization technique.

Critical Hagedorn temperature is derived for a two-piece string.

Abstract

The Casimir energy for the transverse oscillations of a piecewise uniform closed string is calculated. The great adaptability 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 more so the larger is the number of pieces in the string. The thermodynamic free energy and the critical Hagedorn temperature are calculated for a two-piece string. Mass and decay spectra are calculated for quantum massive excitations and the physical meaning of the critical temperatures characterizing the radiation in the decay of a massive microstate is discussed.