Stress energy tensor renormalization for a spherically symmetric massive scalar field on a quantum space-time

TL;DR

This paper explores how a massive scalar field on a quantum space-time from loop quantum gravity can be naturally regularized, with divergences eliminated through finite renormalization, illustrating quantum field theory behavior on quantum geometries.

Contribution

It demonstrates the regularization of a scalar field on a quantum space-time and discusses how to remove micro physics dependence via finite renormalization.

Findings

Discreteness of quantum space-time regularizes the scalar field.

Finite renormalization can remove micro physics dependence.

Quantum space-times address divergences in quantum field theories.

Abstract

We consider a massive scalar field living on the recently found exact quantum space-time corresponding to vacuum spherically symmetric loop quantum gravity. The discreteness of the quantum space time naturally regularizes the scalar field, eliminating divergences. However, the resulting finite theory depends on the details of the micro physics. We argue that such dependence can be eliminated through a finite renormalization and discuss its nature. This is an example of how quantum field theories on quantum space times deal with the issues of divergences in quantum field theories.