Noncommutativity and Parametrization of Fields: The Scalar Electrodynamics Case

Abstract

The aim of this paper is to review the formalism of noncommutativity using canonical parametrization theory. In the first part we present the formalism for the case of Quantum Mechanics, and we show that using this approach and an appropriate basis we can get the noncommutativity expressed in terms of the Moyal product from the Dirac brackets of an extended phase space. We generalize our formalism to the context of Quantum Field Theory where we discuss the case of scalar electrodynamics. The interesting result is that our approach works correctly when we consider an interaction term between the gauge field and the scalar field. Finally, we present an argument that shows that gauge theories are not deformed if we use only noncommutativity of the coordinates. Mathematics Subject Classification (2000). Primary 70S10, 70S05; Secondary 81T75, 20C20.