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Simplicial gauge theory on spacetime

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Abstract

We define a discrete gauge-invariant Yang–Mills–Higgs action on spacetime cylindrical meshes with simplicial spatial base. The formulation is a generalization of classical lattice gauge theory, and we prove consistency of the action in the finite element sense. In addition, we perform numerical tests of convergence towards exact continuum results for several choices of gauge fields in pure gauge theory.

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Notes

  1. Albeit without a scalar potential.

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Acknowledgments

T. G. Halvorsen had funding from SPADE-ACE (Project 176891/V30, The Research Council of Norway). We would like to thank S. H. Christiansen for fruitful discussions.

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  1. Centre of Mathematics for Applications, University of Oslo, Blindern, P. O. Box 1053, 0316 , Oslo, Norway

    Tore Gunnar Halvorsen & Torquil Macdonald Sørensen

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  1. Tore Gunnar Halvorsen
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  2. Torquil Macdonald Sørensen
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Correspondence to Torquil Macdonald Sørensen.

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Halvorsen, T.G., Sørensen, T.M. Simplicial gauge theory on spacetime. Numer. Math. 125, 733–760 (2013). https://doi.org/10.1007/s00211-013-0552-6

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