Deformed Schrodinger symmetry on noncommutative space

TL;DR

This paper develops a deformed Schrödinger symmetry framework compatible with noncommutative space, analyzing free particles and harmonic oscillators, and introduces a generalized Galilean algebra with a universal second central extension.

Contribution

It constructs the deformed Schrödinger generators for noncommutative space and introduces a generalized Galilean algebra with a second central extension in all dimensions.

Findings

Deformed Schrödinger symmetry generators are consistent with noncommutative space.

The generalized Galilean algebra includes a second central extension in all dimensions.

The algebra can be derived from a contraction of a generalized Poincaré algebra.

Abstract

We construct the deformed generators of Schroedinger symmetry consistent with noncommutative space. The examples of the free particle and the harmonic oscillator, both of which admit Schroedinger symmetry, are discussed in detail. We construct a generalised Galilean algebra where the second central extension exists in all dimensions. This algebra also follows from the Inonu--Wigner contraction of a generalised Poincare algebra in noncommuting space.