PRINCIPLES OF DISCRETE-TIME MECHANICS .2. CLASSICAL FIELD-THEORY

We apply the principles discussed in an earlier paper to the construct ion of discrete time field theories. We derive the discrete time held equations of motion and Noether's theorem and apply them to the Schrod inger equation to illustrate the methodology Stationary solutions to t he discrete time Schrodinger wave equation are found to be identical t o standard energy eigenvalue solutions except for a fundamental limit on the energy. Then we apply the formalism to the free neutral Klein-G ordon system, deriving the equations of motion and conserved quantitie s such as the linear momentum and angular momentum. We show that there is an upper bound on the magnitude of linear momentum for physical pa rticle-like solutions. We extend the formalism to the charged scalar f ield coupled to Maxwell's electrodynamics in a gauge invariant way. We apply the formalism to include the Maxwell and Dirac fields, setting the scene for second quantization of discrete time mechanics and discr ete time quantum electrodynamics.