Planck-scale-deformed relativistic symmetries and diffeomorphisms in momentum space

TL;DR

This paper investigates how changing the coordinate system in curved momentum space affects physical predictions in theories with deformed relativistic symmetries, revealing that active diffeomorphisms can alter observable outcomes.

Contribution

It demonstrates that momentum-space covariance cannot be fully enforced, and physical predictions depend on the chosen momentum space background within certain theoretical frameworks.

Findings

Passive diffeomorphisms leave physical predictions unchanged.

Active diffeomorphisms can alter physical predictions.

Dependence on momentum space background in a toy model.

Abstract

We study the implications of a change of coordinatization of momentum space for theories with curved momentum space. We of course find that after a passive diffeomorphism the theory yields the same physical predictions, as one would expect considering that a simple reparametrization should not change physics. However, it appears that general momentum-space covariance (invariance under active diffeomorphisms of momentum space) cannot be enforced, and within a given set of prescriptions on how the theory should encode momentum-space metric and affine connection the physical predictions do depend on the momentum space background. These conclusions find support in some general arguments and in our quantitative analysis of a much-studied toy model with maximally-symmetric (curved) momentum space.