Fundamental Commutators in a Gravitational Field

TL;DR

This paper introduces a novel extension of the Heisenberg commutation relations within a non-commutative space-time framework, utilizing an invariance property of the massless particle action in a gravitational context.

Contribution

It presents a new method to derive extended commutation relations by exploiting invariance properties of massless particles in gravitational fields.

Findings

Extended Heisenberg relations in non-commutative space-time

Method based on invariance of massless particle action

Potential implications for quantum gravity theories

Abstract

We show how an induced invariance of the massless particle action can be used to construct an extension of the Heisenberg canonical commutation relations in a non-commutative space-time.