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The Computation of characteristic classes of lattice gauge fields

Authors
  • Phillips, A.V.
  • Stone, D.A.
Publication Date
Jan 01, 1990
Identifiers
DOI: 10.1007/BF02161414
OAI: oai:inspirehep.net:304730
Source
INSPIRE-HEP
Keywords
License
Unknown
External links

Abstract

AGL(p,C)-valued lattice gauge fieldu on a simplicial complex determines a principalGL(p,C)-bundle ξ if the plaquette products are sufficiently small with respect to the maximum distortion coefficient of the transporters. A representative cocyclecq for theqth Chern class of ξ can be computed on each 2q-simplex σ by takingcq(σ) to be the intersection number of a certain singular 2q-cubeMσ with a Schubert-type variety Σq in the space of allp×p matrices. This reduces to the solution of polynomial equations with coefficients coming fromu and thus avoids numerical integration or cooling-type procedures. An application of this method is suggested for the computation of the topological charge of anSU(3)-valued lattice gauge field on a 4-complex.

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