Effective action of quantum fields in the space-time of a cylindrically symmetric spinning body

TL;DR

This paper computes the first-order quantum effective action of a self-interacting scalar field in the spacetime of a rotating cylindrical body, revealing new ultraviolet divergences and employing regularization and renormalization techniques.

Contribution

It introduces a method to calculate the renormalized effective action for quantum fields in cylindrically symmetric rotating spacetimes, including interior and exterior models.

Findings

Discovery of new ultra-violet poles in the heat kernel

Regularized and renormalized the Klein-Gordon determinant

Analyzed a conical singularity with flux as a test case

Abstract

The aim of this article is to calculate (to first order in $\hbar$) the renormalized effective action of a self interacting massive scalar field propagating in the space-time due to a cylindrically symmetric, rotating body. The vacuum (exterior space-time) contribution is model independent, we also consider the simplest case of a core (interior space-time) model, namely a cylindrical shell. The heat kernel of the system is calculated, and used to obtain an expression for the determinant of the Klein-Gordon operator on the space-time manifold. New ultra-violet poles are discovered, and regularization techniques are then employed to render finite the Klein-Gordon determinant and consequently extract the regularized one loop effective action for a self interacting scalar field theory. The coupling constants of the theory are then renormalized. As a test case a conical singularity with non-zero flux is also considered.