Abelian representation for the non-Abelian Wilson loop and the non-Abelian Stokes theorem on the lattice

2002/12/31 by M. A. Zubkov · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Matrix Theory and Algorithms #Quantum chaos and dynamical systems #hep-lat

paper · pdf · doi:10.1103/physrevd.68.054503

published as Phys.Rev. D68 (2003) 054503 · revtex, 10 pages, ITEP-LAT/2002-36

openalex publication_date 2003/09/12 · arxiv created 2003/09/15 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We derive the Abelian-like expression for the lattice SU(N) Wilson loop in an arbitrary irreducible representation. The continuum Abelian representation of the SU(N) Wilson loop (for the loop without self-intersections) that has been obtained by Diakonov and Petrov appears to be a continuum limit of this expression. We also obtain the lattice variant of a non-Abelian Stokes theorem and present the explicit expression for the matrix H used in the Diakonov-Petrov approach.

Citations

• Quarks, Gluons and Lattices

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