Quantum scalar fields in the half-line. A heat kernel/zeta function approach

TL;DR

This paper analyzes vacuum fluctuations of a scalar field with boundary conditions using heat kernel and zeta function methods, providing explicit spectral function calculations in a finite line.

Contribution

It introduces a novel approach to compute spectral functions for scalar fields with boundary conditions using advanced special functions.

Findings

Explicit formulas for heat kernel and zeta functions in terms of special functions

Spectral analysis of scalar fields with Dirichlet boundary conditions

Connections between spectral functions and boundary effects

Abstract

In this paper we shall study vacuum fluctuations of a single scalar field with Dirichlet boundary conditions in a finite but very long line. The spectral heat kernel, the heat partition function and the spectral zeta function are calculated in terms of Riemann Theta functions, the error function, and hypergeometric PFQ functions.