Noncommutativity from Embedding Techniques

TL;DR

This paper explores how embedding techniques reveal noncommutative structures in the Landau problem, showing that different gauge choices lead to various noncommutative algebras and discussing implications for non-uniform magnetic fields.

Contribution

It demonstrates the application of Batalin-Tyutin embedding to uncover noncommutative geometries and establishes a duality among different algebraic structures in the Landau problem.

Findings

Different gauge choices produce distinct noncommutative algebras.

Embedding method and alternative approaches yield equivalent results.

Implications for non-constant magnetic fields are discussed.

Abstract

We apply the embedding method of Batalin-Tyutin for revealing noncommutative structures in the generalized Landau problem. Different types of noncommutativity follow from different gauge choices. This establishes a duality among the distinct algebras. An alternative approach is discussed which yields equivalent results as the embedding method. We also discuss the consequences in the Landau problem for a non constant magnetic field.