Galilean symmetry in noncommutative Gravitational Quantum Well

TL;DR

This paper analyzes Galilean symmetries in a noncommutative gravitational quantum well, demonstrating algebra closure and linking the model to experimental bounds on noncommutativity, with noncommutativity increasing gravitational pull.

Contribution

It establishes the complete Galilean symmetry algebra for the noncommutative gravitational well and confirms the model's coordinate independence, connecting theory with experimental bounds.

Findings

Galilean algebra is fully realized in the noncommutative model

The model's energy spectrum aligns with experimental data

Noncommutativity enhances gravitational attraction in the system

Abstract

A thorough analysis of Galilean symmetries for the gravitational well problem on a noncommutative plane is presented. A complete closure of the one-parameter centrally extended Galilean algebra is realised for the model. This implies that the field theoretic model constructed to describe noncommutative gravitational quantum well in \cite{ani} is indeed independent of the coordinate choice. Hence the energy spectrum predicted by the model can be associated with the experimental results to establish the upper-bound on time-space noncommutative parameter. Interestingly, noncommutativity is shown to increase the gravitational pull on the neutron trapped in the gravitational well.