Noncommutative gauge theories
The present work is devoted to study the semi-classical limit of full noncommutative gauge theory, known as Poisson gauge theory. First we construct an L$_{\infty}^{full}$ algebra which governs both the action of gauge symmetries and the dynamics of the theory, deriving a set of non-vanishing brackets, and proving that they satisfy the corresponding homotopy relations. Then we use the pure spatial canonical non-commutativity to investigate the effects of wave propagation under an external magnetic field, obtaining properties of the medium ruled by the permittivity and the permeability tensors in terms of the non-commutative parameter, and the birefringence phenomenon emerged from the modified dispersion relations. Finally, we attempt to construct the non-associative gauge theory using a quasi-Poisson structure isomorphic to the Malcev algebra of octonions.