Discrete Field Theory: Symmetries and Conservation Laws

Mikhail Skopenkov

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish (US)
JournalMathematical Physics Analysis and Geometry
Issue number3
StatePublished - Aug 3 2023

ASJC Scopus subject areas

  • Mathematical Physics
  • Geometry and Topology


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