Algebraic approach to multiple defects on the line and application to Casimir force

TL;DR

This paper develops an algebraic framework for quantizing scalar fields with multiple point-like defects on a line and applies it to compute Casimir forces and charge densities at various temperatures.

Contribution

It introduces a novel algebraic approach for quantization in the presence of multiple defects and applies it to Casimir force calculations and charge density analysis.

Findings

Casimir force computed at zero and finite temperature.

Charge density in Gibbs state derived for complex scalar fields.

Detailed analysis of two delta-defects case.

Abstract

An algebraic framework for quantization in presence of arbitrary number of point-like defects on the line is developed. We consider a scalar field which interacts with the defects and freely propagates away of them. As an application we compute the Casimir force both at zero and finite temperature. We derive also the charge density in the Gibbs state of a complex scalar field with defects. The example of two delta-defects is treated in detail.