Poisson Electrodynamics and Applications

Abstract

Constructing gauge theories on non-commutative spaces of general form is a notoriously difficult problem which attracts attention of theoretical physicists and mathematicians for more then two decades. Nevertheless, it is still not completely understood in full generality. Poisson electrodynamics is a semi-classical limit of non-commutative U(1) gauge theory. In recent years we have formulated three new approaches to consistent non-commutative and even non-associative deformations of gauge theory. The first one employs the framework of homotopy algebras and is a powerful tool for the construction of order by order non-commutative deformation. The second and the third approaches make use of the elements from the symplectic geometry and are better adapted for obtaining of the explicit all-order expressions as well as understanding of geometric nature of the obtained models. Several interesting results have been obtained and published in this direction. In this project we briefly describe the three approaches and formulate the topics of the future research, including the further development of the mathematical formalism and its application to the investigation of physical effects caused by the non-commutativity. (AU)