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Electromagnetic Dualities on Noncommutative Space-Time and Symplectic Formalisms

Davi C. Rodrigues
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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.

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Davi C. Rodrigues. 2006-11-07. Electromagnetic Dualities on Noncommutative Space-Time and Symplectic Formalisms. https://arxiv.org/abs/hep-th/0611073

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