Diffeomorphisms in momentum space: physical implications of different choices of momentum coordinates in the Galilean Snyder model

TL;DR

This paper investigates how different momentum coordinate choices in the Galilean Snyder noncommutative spacetime affect physical predictions, demonstrating that they lead to distinct energy spectra for the harmonic oscillator.

Contribution

It analyzes the impact of momentum space diffeomorphisms on physical predictions within the Galilean Snyder model, highlighting differences in energy spectra.

Findings

Different momentum space choices yield distinct harmonic oscillator spectra.

Diffeomorphisms in momentum space can alter physical predictions.

Not all momentum coordinate choices are physically equivalent.

Abstract

It has been pointed out that different choices of momenta can be associated to the same noncommutative spacetime model. The question of whether these momentum spaces, related by diffeomorphisms, produce the same physical predictions is still debated. In this work, we focus our attention on a few different momentum spaces that can be associated to the Galilean Snyder noncommutative spacetime model and show that they produce different predictions for the energy spectrum of the harmonic oscillator.