Discrete field theory: symmetries and conservation laws
arXiv:1709.04788 · doi:10.1007/s11040-023-09459-4
Abstract
We present a general algorithm constructing a discretization of a classical field theory from a Lagrangian. We prove a new discrete Noether theorem relating symmetries to conservation laws and an energy conservation theorem not based on any symmetry. This gives exact conservation laws for several theories, e.g., lattice electrodynamics and gauge theory. In particular, we construct a conserved discrete energy-momentum tensor, approximating the continuum one at least for free fields. The theory is stated in topological terms, such as coboundary and products of cochains.
46 pages, 10 figures; exposition improved: more detailed comparison to the existing literature added, text reordered to minimize forward references
References in corpus (6)
- Variational Integrators for Nonvariational Partial Differential Equations
- Diffusion in multi-dimensional solids using Forman's combinatorial differential forms
- Discrete stress-energy tensor in the loop O(n) model
- Energy--momentum tensor on the lattice: recent developments
- Discrete analytic functions on non-uniform lattices without global geometric control
- Discrete field theory: symmetries and conservation laws