Quantum Field Theory in a Multi-Metric Background

TL;DR

This paper explores the challenges of quantizing interacting quantum fields in multi-metric backgrounds, focusing on causality, renormalization, and Lorentz symmetry within simple flat spacetime models.

Contribution

It introduces an interpolating metric to analyze causality and studies the renormalization group structure, highlighting effects on Lorentz symmetry in multi-metric quantum field theories.

Findings

Interpolating metric helps maintain causality in multi-metric models

Renormalization group analysis reveals Lorentz symmetry breakdown

Quartic interaction models exhibit specific renormalization behaviors

Abstract

By means of simple models in a flat spacetime manifold we examine some of the issues that arise when quantizing interacting quantum fields in multi-metric backgrounds. In particular we investigate the maintenance of a causal structure in the models. In this context we introduce and explain the relevance of an interpolating metric that is a superposition of the individual metrics in the models. We study the renormalisation of a model with quartic interactions and elucidate the structure of the renormalisation group and its implications for Lorentz symmetry breakdown.