Casimir Energies in the Light of Renormalizable Quantum Field Theories

TL;DR

This paper introduces efficient methods for calculating renormalized Casimir energies in quantum field theories and applies them to construct soliton solutions, advancing understanding of quantum fluctuations and boundary effects.

Contribution

It presents new computational techniques for one-loop vacuum energies and applies them to soliton construction within a variational framework.

Findings

Developed methods for calculating renormalized Casimir energies

Applied techniques to construct soliton solutions

Analyzed singular limits in classical Casimir problems

Abstract

Effective hadron models commonly require the computation of functional determinants. In the static case these are one--loop vacuum polarization energies, known as Casimir energies. In this talk I will present general methods to efficiently compute renormalized one--loop vacuum polarization energies and energy densities and apply these methods to construct soliton solutions within a variational approach. This calculational method is particularly useful to study singular limits that emerge in the discussion of the {\it classical} Casimir problem which is usually posed as the response of a fluctuating quantum field to externally imposed boundary conditions.