Twisted Galilean symmetry and the Pauli principle at low energies

TL;DR

This paper demonstrates the twisted Galilean invariance in noncommutative space-time, derives the deformed Schrödinger algebra, and assesses the impact on the Pauli principle, finding effects likely undetectable at current energies.

Contribution

It introduces a deformed algebra for the Schrödinger field under twisted Galilean symmetry and evaluates its implications for the Pauli principle at low energies.

Findings

Twisted Galilean invariance holds even with space-time noncommutativity.

Deformed algebra of the Schrödinger field is derived.

Possible violations of the Pauli principle are negligible at current energies.

Abstract

We show the twisted Galilean invariance of the noncommutative parameter, even in presence of space-time noncommutativity. We then obtain the deformed algebra of the Schr\"odinger field in configuration and momentum space by studying the action of the twisted Galilean group on the non-relativistic limit of the Klein-Gordon field. Using this deformed algebra we compute the two particle correlation function to study the possible extent to which the previously proposed violation of the Pauli principle may impact at low energies. It is concluded that any possible effect is probably well beyond detection at current energies.