One-loop stress tensors for scalar and spinor fields on the homogeneous spaces with G-invariant metrics

TL;DR

This paper computes the vacuum expectation value of the stress-energy tensor for scalar and spinor fields on homogeneous spaces with G-invariant metrics using coadjoint orbits and harmonic analysis.

Contribution

It introduces a method to calculate stress tensors on homogeneous spaces employing coadjoint orbits and harmonic analysis, extending previous techniques.

Findings

Explicit formulas for stress tensors on homogeneous spaces.

Application to scalar and spinor fields.

Framework for future quantum field theory calculations on curved spaces.

Abstract

Vacuum expectation value of the stress-energy-momentum tensor for scalar and spinor fields is obtainted on the homogeneous space with $G$-invariant metrics using the orbits of coadjoint representation of Lie group and the generalized harmonic analysis.