# Vacuum quantum effects on Lie groups with bi-invariant metrics

## TL;DR

This paper investigates how vacuum polarization and particle creation of a scalar field influence Lie groups with non-stationary bi-invariant metrics, using noncommutative integration, exemplified by the 3D rotation group.

## Contribution

It introduces a novel approach using noncommutative integration to compute vacuum effects on Lie groups with dynamic metrics, expanding understanding beyond traditional methods.

## Key findings

- Vacuum expectation values are explicitly calculated for scalar fields on Lie groups.
- The noncommutative integration method effectively replaces separation of variables.
- Results are demonstrated with the three-dimensional rotation group example.

## Abstract

We consider the effects of vacuum polarization and particle creation of a scalar field on Lie groups with a non-stationary bi-invariant metric of the Robertson-Walker type. The vacuum expectation values of the energy momentum tensor for a scalar field determined by the group representation are found using the noncommutative integration method for the field equations instead of separation of variables. The results obtained are illustrated by the example of the three-dimensional rotation group.