Lorentz symmetry breaking as a quantum field theory regulator

TL;DR

This paper investigates using Lorentz symmetry breaking as a novel regularization method in quantum field theories, demonstrating its potential to regulate divergences without compromising the theory's logical consistency.

Contribution

It introduces a Lorentz symmetry breaking regulator in a scalar field theory and analyzes its effectiveness and implications, connecting to quantum gravity approaches.

Findings

Lorentz symmetry breaking can fully regulate the scalar field theory.

The required degree of symmetry breaking is quantified.

Insights relate to Horava's quantum gravity model.

Abstract

Perturbative expansions of relativistic quantum field theories typically contain ultraviolet divergences requiring regularization and renormalization. Many different regularization techniques have been developed over the years, but most regularizations require severe mutilation of the logical foundations of the theory. In contrast, breaking Lorentz invariance, while it is certainly a radical step, at least does not damage the logical foundations of the theory. We shall explore the features of a Lorentz symmetry breaking regulator in a simple polynomial scalar field theory, and discuss its implications. We shall quantify just "how much" Lorentz symmetry breaking is required to fully regulate the theory and render it finite. This scalar field theory provides a simple way of understanding many of the key features of Horava's recent article [arXiv:0901.3775 [hep-th]] on 3+1 dimensional quantum gravity.