Casimir energy of a non-uniform string

TL;DR

This paper calculates the Casimir energy of a non-uniform string composed of two segments with different sound speeds, demonstrating a renormalization approach and its equivalence to zeta function regularization in the homogeneous case.

Contribution

It introduces a method to compute Casimir energy for non-uniform strings and compares it with zeta renormalization, extending understanding of quantum effects in inhomogeneous systems.

Findings

Casimir energy for non-uniform string derived

Renormalization method aligns with zeta regularization for homogeneous strings

Provides a framework for analyzing quantum energies in composite strings

Abstract

The Casimir energy of a non-uniform string built up from two pieces with different speed of sound is calculated. A standard procedure of subtracting the energy of an infinite uniform string is applied, the subtraction being interpreted as the renormalization of the string tension. It is shown that in the case of a homogeneous string this method is completely equivalent to the zeta renormalization.