Discrete-time quantum mechanics. III. Spin systems

A program is underway to obtain numerical solutions to quantum field theories by formulating them in terms of operator difference equations on a Minkowski space-time lattice. The most crucial unsolved problem is implementing non-Abelian gauge invariance. This paper initiates the study of this difficult problem by treating spin systems. The central problem here is to preserve exactly the (q-number) non-Abelian commutation relations at each lattice site. The solution we propose requires that the spin variables be expressed in terms of more fundamental oscillator variables which satisfy the Heisenberg algebra.