Note on the point-splitting procedure to evaluate vacuum fluctuation in certain cylindrically symmetric backgrounds

TL;DR

This paper examines the point-splitting method for evaluating vacuum fluctuations in cylindrically symmetric spacetimes, addressing divergence issues and applying it to a massless scalar field around cosmic strings.

Contribution

It provides a detailed analysis of divergence handling in the point-splitting procedure within wedge-shaped and conical backgrounds, specifically for cosmic string spacetimes.

Findings

Divergent integrals in vacuum fluctuation calculations are identified and addressed.

The approach is applied to a massless scalar field in cosmic string spacetime.

Insights into the regularization of vacuum fluctuations in cylindrically symmetric backgrounds.

Abstract

We revisit two-point function approaches used to study vacuum fluctuation in wedge-shaped regions and conical backgrounds. Appearance of divergent integrals is discussed and circumvented. The issue is considered in the context of a massless scalar field in cosmic string spacetime.