Properties of a Discrete Quantum Field Theory
  A scalar quantum field theory defined on a discrete spatial coordinate is examined. The renormalization of the lattice propagator is discussed with an emphasis on the periodic nature of the associated momentum coordinate. The analytic properties of the scattering amplitudes indicate the development of a second branch point on which the branch cut from the optical theorem terminates. 
Micheal S. Berger and Naoki Yamatsu
hep-th hep-ph