Field Theory with Coordinate Dependent Noncommutativity

Abstract

We discuss the formulation of classical field theoretical models on n-dimensional noncommutative space-time defined by a generic associative star product. A simple procedure for deriving conservation laws is presented and applied to field theories in noncommutative space-time to obtain local conservation laws (for the electric charge and for the energy-momentum tensor of free fields) and, more generally, an energy-momentum balance equation for interacting fields. For free field models, an analogy with the damped harmonic oscillator in classical mechanics is pointed out, which allows us to get a physical understanding of the obtained conservation laws. To conclude, the formulation of field theories on curved noncommutative space is addressed.