Microcausality in Curved Space-Time

TL;DR

This paper demonstrates that microcausality, the vanishing commutator of space-like operators, is rooted in classical causal structure and holds in curved space-times even without Lorentz invariance, supported by explicit calculations.

Contribution

It provides two arguments showing microcausality is due to classical causality, not Lorentz invariance, extending its validity to arbitrary curved space-times.

Findings

Microcausality holds in curved space-times without Lorentz invariance.

Explicit Feynman diagram calculations confirm microcausality in non-flat backgrounds.

Classical causal structure underpins quantum microcausality in curved geometries.

Abstract

It is well known that in Lorentz invariant quantum field theories in flat space the commutator of space-like separated local operators vanishes (microcausality). We provide two different arguments showing that this is a consequence of the causal structure of the classical theory, rather than of Lorentz invariance. In particular, microcausality holds in arbitrary curved space-times, where Lorentz invariance is explicitly broken by the background metric. As illustrated by an explicit calculation on a cylinder this property is rather non trivial at the level of Feynman diagrams.