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

作者：Das A^*

来源：Canadian Journal of Physics, 2010, 88(2): 73-91.

DOI：10.1139/P09-089

This is the first in a series of papers dealing with a discrete phase space formulation for classical and quantum fields. This formulation leads to a representation of quantum field theory that is covariant and possesses singularity free S-matrix. In this paper, 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.

• 出版日期2010-2