On the path integral representation for the Wilson loop and the non-Abelian Stokes theorem

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dc.creatorFaber, M.
dc.creatorIvanov, A. N.
dc.creatorTroitskaya, N. I.
dc.creatorZach, M.
dc.date1999-07-08
dc.date2000-05-17
dc.date.accessioned2026-07-07T11:36:23Z
dc.date.available2026-07-07T11:36:23Z
dc.descriptionWe discuss the derivation of the path integral representation over gauge degrees of freedom for Wilson loops in SU(N) gauge theory and 4-dimensional Euclidean space-time by using well-known properties of group characters. A discretized form of the path integral is naturally provided by the properties of group characters and does not need any artificial regularization. We show that the path integral over gauge degrees of freedom for Wilson loops derived by Diakonov and Petrov (Phys. Lett. B224 (1989) 131) by using a special regularization is erroneous and predicts zero for the Wilson loop. This property is obtained by direct evaluation of path integrals for Wilson loops defined for pure SU(2) gauge fields and Z(2) center vortices with spatial azimuthal symmetry. Further we show that both derivations given by Diakonov and Petrov for their regularized path integral, if done correctly, predict also zero for Wilson loops. Therefore, the application of their path integral representation of Wilson loops cannot give "a new way to check confinement in lattice" as has been declared by Diakonov and Petrov (Phys. Lett. B242 (1990) 425). From the path integral representation which we consider we conclude that no new non-Abelian Stokes theorem can exist for Wilson loops except the old-fashioned one derived by means of the path-ordering procedure.
dc.description33 pages, no figures, Latex, the explicit evaluations of the path integrals suggested by Diakonov and Petrov for the Wilson loop are added. It is shown that path integrals have been evaluated by Diakonov and Petrov incorrectly and the path integral representation for the Wilson loop is erroneous. Therefore, the path integral representation for the Wilson loop invented by Diakonov and Petrov cannot give "a new way to check confinement in lattice"
dc.identifierhttps://arxiv.org/abs/hep-th/9907048
dc.identifierhttp://arxiv.org/abs/hep-th/9907048
dc.identifierPhys.Rev.D62:025019,2000
dc.identifierdoi:10.1103/PhysRevD.62.025019
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/198904
dc.subjectHigh Energy Physics - Theory
dc.titleOn the path integral representation for the Wilson loop and the non-Abelian Stokes theorem
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