Canonical analysis of space-time noncommutative theories and gauge symmetries

We construct a modification of the Poisson bracket which is suitable for a canonical analysis of space-time noncommutative field theories. We show that this bracket satisfies the Jacobi identities and generates equations of motion. In this modified canonical formalism one can define the notion of the first-class constraints, demonstrate that they generate gauge symmetries, and derive an explicit form of these symmetry transformations.