QUANTUM ELECTRODYNAMICS ON A SPACE-TIME LATTICE

A Minkowski-lattice version of quantum electrodynamics (or rather its simplified version, with matter described by a scalar field) is constr ucted. Quantum fields are consequently described in a gauge-independen t way, i.e. the algebra of quantum observables of the theory is genera ted by gauge-invariant operators assigned to zero-, one-, and two-dime nsional elements of the lattice. The operators satisfy canonical commu tation relations. The uniqueness of representation of this algebra is proved. Field dynamics is formulated in terms of difference equations imposed on the held operators. It is obtained from a discrete version of the path-integral. The theory is local and causal.