q-deformed Phase Space and its Lattice Structure

TL;DR

This paper explores a q-deformed two-dimensional phase space as a model for noncommutative geometry, revealing a lattice structure that signifies spontaneous symmetry breaking and deriving eigenfunctions for Hamiltonians on this lattice.

Contribution

It introduces a novel q-deformed phase space model with an emergent lattice structure and derives eigenfunctions within this framework.

Findings

Lattice structure emerges from q-deformation

Eigenfunctions are derived for Hamiltonians on the lattice

Spontaneous symmetry breaking is interpreted in the model

Abstract

A q-deformed two-dimensional phase space is studied as a model for a noncommutative phase space. A lattice structure arises that can be interpreted as a spontaneous breaking of a continuous symmetry. The eigenfunctions of a Hamiltonian that lives on such a lattice are derived as wavefunctions in ordinary $x$-space.