Time-Space Noncommutativity in Gravitational Quantum Well scenario

TL;DR

This paper introduces a second quantised framework to analyze time-space noncommutativity effects in gravitational quantum wells, providing new insights and bounds consistent with previous estimates.

Contribution

It presents the first second quantised formalism for gravitational wells to incorporate time-space noncommutativity effects, deriving perturbation terms and experimental bounds.

Findings

Derived a leading order perturbation term of noncommutative origin.

Estimated an upper bound on the time-space noncommutative parameter.

Results align with previous magnitude estimations of noncommutative parameters.

Abstract

A novel approach to the analysis of the gravitational well problem from a second quantised description has been discussed. The second quantised formalism enables us to study the effect of time space noncommutativity in the gravitational well scenario which is hitherto unavailable in the literature. The corresponding first quantized theory reveals a leading order perturbation term of noncommutative origin. Latest experimental findings are used to estimate an upper bound on the time--space noncommutative parameter. Our results are found to be consistent with the order of magnitude estimations of other NC parameters reported earlier.