The Second Order Effect of the Quantum Weyl Algebra on a Free Particle

TL;DR

This paper explores how second-order effects of the quantum Weyl algebra influence a free particle, revealing emergent magnetic fields and anisotropic effects through a deformed coordinate system expansion.

Contribution

It provides a concrete realization of a deformed coordinate system using a q-parameter expansion, extending previous work on quantum Weyl algebra effects on free particles.

Findings

First-order expansion yields a constant magnetic field.

Second-order expansion reveals an anisotropic magnetic field.

Identifies quantum symmetries within the quantum Weyl algebra.

Abstract

In this paper we revisit and extend the work done by Chaturvedu et al, as well as Dabrowski and Parashar. The basic premise is to take a deformed coordinate system and give is a concrete realization. This realization is given by a parameter of q = exp (it). Expanding in powers of 't' and applying a deformed quantum Hamiltonian to a Free Particle yields a magnetic field. To first order we recover a constant magnetic field. To second order we recover an anisotropic magnetic field with an additional term. A brief mention is made about the quantum symmetries present within the quantum Weyl algebra.