Generalized Bogoliubov Transformation for Confined Fields: Applications in Casimir Effect

TL;DR

This paper generalizes the Bogoliubov transformation within thermofield dynamics to describe confined quantum fields, enabling calculations of the Casimir effect at various temperatures and offering a new approach for studying confined and interacting fields.

Contribution

It introduces a generalized Bogoliubov transformation for confined fields, extending its application to electromagnetic fields and Casimir effect calculations at finite temperatures.

Findings

Casimir effect computed for zero and non-zero temperatures.

The approach models the Casimir effect as a vacuum condensation phenomenon.

Provides a new method for studying confined and interacting quantum fields.

Abstract

The Bogoliubov transformation in thermofield dynamics, an operator formalism for the finite-temperature quantum-field theory, is generalized to describe a field in arbitrary confined regions of space and time. Starting with the scalar field, the approach is extended to the electromagnetic field and the energy-momentum tensor is written via the Bogoliubov transformation. In this context, the Casimir effect is calculated for zero and non-zero temperature, and therefore it can be considered as a vacuum condensation effect of the electromagnetic field. This aspect opens an interesting perspective for using this procedure as an effective scheme for calculations in the studies of confined fields, including the interacting fields.