The time slice axiom in perturbative quantum field theory on globally hyperbolic spacetimes

TL;DR

This paper proves that the time slice axiom, which states that local observables determine all other observables, holds for scalar field theories in perturbative quantum field theory on globally hyperbolic spacetimes.

Contribution

It extends the validity of the time slice axiom from free theories to interacting scalar field theories within formal renormalized perturbation theory.

Findings

The time slice axiom holds for scalar field theories in perturbative quantum field theory.

The proof applies to theories on globally hyperbolic spacetimes.

It broadens understanding of local observables in interacting quantum fields.

Abstract

The time slice axiom states that the observables which can be measured within an arbitrarily small time interval suffice to predict all other observables. While well known for free field theories where the validity of the time slice axiom is an immediate consequence of the field equation it was not known whether it also holds in generic interacting theories, the only exception being certain superrenormalizable models in 2 dimensions. In this paper we prove that the time slice axiom holds at least for scalar field theories within formal renormalized perturbation theory.