Discrete phase space - I: Variational formalism for classical relativistic wave fields

The classical relativistic wave equations are presented as partial difference equations in the arena of covariant discrete phase space. These equations are also expressed as difference-differential equations in discrete phase space and continuous time. The relativistic invariance and covariance of the equations in both versions are established. The partial difference and difference-differential equations are derived as the Euler-Lagrange equations from the variational principle. The difference and difference-differential conservation equations are derived. Finally, the total momentum, energy, and charge of the relativistic classical fields satisfying difference-differential equations are computed. PACS: 11.10.Ef; 11.10.Qr; 11-15.Ha