Vacuum Energy Induced by an External Magnetic Field in a Curved Space

TL;DR

This paper derives an asymptotic expansion to express the vacuum energy density induced by static magnetic fields in curved space, linking it to geometric coefficients for both Abelian and non-Abelian fields.

Contribution

It introduces a new asymptotic expansion method to relate vacuum energy density to DeWitt-Seeley-Gilkey coefficients in curved space with magnetic fields.

Findings

Vacuum energy density expressed in terms of geometric coefficients.

Applicable to both Abelian and non-Abelian magnetic fields.

Provides a mathematical framework for analyzing vacuum energy in curved backgrounds.

Abstract

The asymptotic expansion of the product of an operator raised to an arbitrary power and an exponential function of this operator is obtained. With the aid of this expansion, the density of vacuum energy induced by a static external magnetic field of an Abelian or non-Abelian nature is expressed in terms of the DeWitt-Seeley-Gilkey coefficients.