Reconditioning in Discrete Quantum Field Theory.

We consider a discrete scalar, quantum field theory based on a cubic 4-dimensional lattice. We mainly investigate a discrete scattering operator S( x , r) where x and r are positive integers representing time and maximal total energy, respectively. The operator S( x , r) is used to define transition amplitudes which are then employed to compute transition probabilities. These probabilities are conditioned on the time-energy ( x , r). In order to maintain total unit probability, the transition probabilities need to be reconditioned at each ( x , r). This is roughly analogous to renormalization in standard quantum field theory, except no infinities or singularities are involved. We illustrate this theory with a simple scattering experiment involving a common interaction Hamiltonian. We briefly mention how discreteness of spacetime might be tested astronomically. Moreover, these tests may explain the existence of dark energy and dark matter. [ABSTRACT FROM AUTHOR]