Formal developments in curved momentum space: the quantum field theory roadmap

TL;DR

This paper explores the concept of curved momentum space as a dual to spacetime noncommutativity, proposing a framework for deformed quantum field equations and outlining potential approaches for defining quantum field theories in this context.

Contribution

It introduces a formal framework for quantum field theory on curved momentum space, including deformed Klein-Gordon and Dirac equations, addressing conceptual issues like basis dependence.

Findings

Formulated deformed Klein-Gordon and Dirac equations

Proposed methods for constructing free and interacting quantum field theories

Suggested curved momentum space as a solution to conceptual problems

Abstract

We advocate that the dual picture of spacetime noncommutativity , i.e. the existence of a curved momentum space, could be a way out to solve some of the open conceptual problems in the field, such as the basis dependence of observables. In this framework, we show how to build deformed Klein--Gordon and Dirac equations. In addition, we give an outlook of how one could define quantum field theories, both free and interacting ones.