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Discrete field theory: symmetries and conservation laws

2018

We are going to give a general algorithm constructing a discretization of a classical field theory from a Lagrangian. We are going to prove a discrete Noether theorem relating symmetries to conservation laws and an energy conservation theorem not based on any symmetry. In particular, we are going to find new exact conservation laws for several discrete field theories: electrodynamics, gauge theory, Klein–Gordon and Dirac ones. Also we are going construct a conserved discrete energy-momentum tensor, approximating the continuum one at least for free fields. The theory is going to be stated in topological terms, such as coboundary and products of cochains.