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Lattice gauge fields, principal bundles and the calculation of topological charge

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Abstract

SU2-valued lattice gauge fields are studied on a 4-dimensional simplicial lattice. Ifu has sufficiently small plaquette products, then there is a unique principal SU2-bundle ξ admitting transition functions, defined on the intersections of adjacent dual cells, which take values within π/8 ofu. An algorithm is explicitly given which associates an integer to everyu off a certain set of measure zero. This algorithm only involves evaluation of 4×4 determinants and the solution of quadratic equations. Whenu is as above, the integer produced is the second Chern number of ξ, i.e. the topological charge ofu.

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Authors and Affiliations

  1. Department of Mathematics, State University of New York at Stony Brook, 11794, Stony Brook, NY, USA

    Anthony Phillips

  2. Department of Mathematics, Brooklyn College, 11210, Brooklyn, NY, USA

    David Stone

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  1. Anthony Phillips
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  2. David Stone
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Communicated by K. Osterwalder

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Phillips, A., Stone, D. Lattice gauge fields, principal bundles and the calculation of topological charge. Commun.Math. Phys. 103, 599–636 (1986). https://doi.org/10.1007/BF01211167

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  • DOI: https://doi.org/10.1007/BF01211167

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