Gauge and BRST Generators for Space-Time Non-commutative U(1) Theory

The Hamiltonian (gauge) symmetry generators of non-local (gauge) theories are presented. The construction is based on the d+1 dimensional space-time formulation of d dimensional non-local theories. The procedure is applied to U(1) space-time non-commutative gauge theory. In the Hamiltonian formalism the Hamiltonian and the gauge generator are constructed. The nilpotent BRST charge is also obtained. The Seiberg-Witten map between non-commutative and commutative theories is described by a canonical transformation in the superphase space and in the field-antifield space. The solutions of classical master equations for non-commutative and commutative theories are related by a canonical transformation in the antibracket sense.