Asymptotic Analysis of Field Commutators for Einstein-Rosen Gravitational Waves

TL;DR

This paper analyzes the asymptotic behavior of field commutators in cylindrically symmetric gravitational waves, exploring quantum effects on causality and the semiclassical limit in quantum gravity.

Contribution

It provides a detailed asymptotic analysis of field commutators in a simplified quantum gravity model with cylindrical symmetry, highlighting non-uniform behaviors in the small G limit.

Findings

Field commutators reveal smearing of light cones due to quantum effects.

The small G behavior depends on causal relationships between points.

Large gravitational effects can emerge in this model.

Abstract

We give a detailed study of the asymptotic behavior of field commutators for linearly polarized, cylindrically symmetric gravitational waves in different physically relevant regimes. We also discuss the necessary mathematical tools to carry out our analysis. Field commutators are used here to analyze microcausality, in particular the smearing of light cones owing to quantum effects. We discuss in detail several issues related to the semiclassical limit of quantum gravity, in the simplified setting of the cylindrical symmetry reduction considered here. We show, for example, that the small G behavior is not uniform in the sense that its functional form depends on the causal relationship between spacetime points. We consider several physical issues relevant for this type of models such as the emergence of large gravitational effects.