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Topological charge of (lattice) gauge fields

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Abstract

Using recently derived explicit formulae for the 2- and 3-cochains in SU(2) gauge theory, we are able to integrate the Chern-Simons density analytically. We arrive — in SU(2) — at a local algebraic expression for the topological charge, which is the sum of local winding numbers associated with the corners (lattice points) of the cells covering the manifold plus contributions from possible isolated gauge singularities which manifest themselves as “vortices” in the 1-, 2- or 3-cochains. Among others we consider hypercubic geometry — i.e. covering the manifold by hypercubes — which is of particular interest to lattice Monte Carlo applications. Finally, we extend our results to SU(3) gauge theory.

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Authors and Affiliations

  1. Institut für Theoretische Physik der Universität, D-6900, Heidelberg, Germany

    M. Göckeler

  2. NORDITA, Copenhagen, Denmark

    M. L. Laursen

  3. Institut für Theoretische Physik der Universität, D-2300, Kiel, Germany

    G. Schierholz

  4. Deutsches Elektronen-Synchrotron DESY, D-2000, Hamburg, Germany

    G. Schierholz

  5. Institut für Theoretische Physik der Universität, D-3000, Hannover, Germany

    U. -J. Wiese

Authors
  1. M. Göckeler
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  2. M. L. Laursen
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  3. G. Schierholz
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  4. U. -J. Wiese
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Communicated by G. Mack

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Göckeler, M., Laursen, M.L., Schierholz, G. et al. Topological charge of (lattice) gauge fields. Commun.Math. Phys. 107, 467–481 (1986). https://doi.org/10.1007/BF01221000

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  • DOI: https://doi.org/10.1007/BF01221000

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