Electromagnetic Dualities on Noncommutative Space-Time and Symplectic Formalisms

TL;DR

This thesis explores the extension of electromagnetic dualities to noncommutative space-times in 3D and 4D, analyzing the role of the noncommutativity parameter and developing a gauge embedding technique based on symplectic methods.

Contribution

It extends electromagnetic duality concepts to noncommutative 3D and 4D space-times and introduces a symplectic gauge embedding technique applicable to these models.

Findings

Noncommutativity parameter theta relates to its dual *theta via duality.

Extended duality to 3D space-time with topological mass.

Developed a symplectic gauge embedding method for noncommutative models.

Abstract

In this thesis we analyze extensions of classical electromagnetic dualities to the noncommutative (NC) 3D and 4D space-times. It is known that the noncomutativity parameter theta becomes its Hodge dual *theta through the NC 4D electromagnetic duality [under the Slowly Varying Fields (SVF) limit], this is a nontrivial transformation which connects noncommutativity in space with noncommutativity between space and time. In this thesis we extend this duality to the 3D space-time, evaluate the necessity of the SVF limit in both 4D and 3D, study the 3D case with topological mass and establish a noncommutative extension to the selfdual model, clarifying certain conflicts found in the literature. We also present here the development of a technique of gauge embedding inspired in the symplectic handling of constraints which has already been applied to a number of models, both commutative and noncommutative, and success has been achieved in reproducing results obtained by other methods.