Discrete Differential Geometry and Lattice Field Theory

2003/12/31 by Miguel Lorente, M. Lorente, Lorente, M.
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #Geometric and Algebraic Topology #High Energy Physics - Lattice (hep-lat) #advanced mathematical theories #hep-lat

paper · pdf · doi:10.48550/arxiv.hep-lat/0312045

Proceedings: A. W. Sissakian, G. S. Pogosian eds. VII International Conference on Symmetry Methods in Physics (J.I.N.R. Dubna 1996) pp. 368-377. LaTeX, 11 pages (late submission)

arxiv created 2003/12/31 · openalex publication_date 2003/12/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develope a difference calculus analogous to the differential geometry by translating the forms and exterior derivatives to similar expressions with difference operators, and apply the results to fields theory on the lattice [Ref. 1]. Our approach has the advantage with respect to other attempts [Ref. 2-6] that the Lorentz invariance is automatically preserved as it can be seen explicitely in the Maxwell, Klein-Gordon and Dirac equations on the lattice.

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