Relative partition function of Coulomb plus delta interaction

TL;DR

This paper investigates the mathematical properties of the relative partition and zeta functions for a Laplace operator perturbed by Coulomb and point interactions, with implications for Casimir effect studies.

Contribution

It introduces a detailed analysis of the relative partition and zeta functions for Coulomb plus delta interactions, extending spectral theory methods.

Findings

Derived explicit formulas for the relative partition function.

Analyzed the spectral properties of the perturbed Laplace operator.

Discussed applications to Casimir effect calculations.

Abstract

The relative partition function and the relative zeta function of the perturbation of the Laplace operator by a Coulomb potential plus a point interaction centered in the origin is discussed. Applications to the study of the Casimir effect are indicated.