Polygon discretization of the loop-space equation

Methods for studying equations on the loop space are developed using interpretation of the loop equation of many-color QCD as the functional (inhomogeneous) Laplace equation. We discretize the loop space by M-vertex polygons to approximate the functional laplacian by a (finite-dimensional) second or...

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Bibliographic Details
Published in:Physics letters. B 1988-09, Vol.212 (2), p.221-226
Main Author: Makeenko, Yu.M.
Format: Article
Language:English
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Summary:Methods for studying equations on the loop space are developed using interpretation of the loop equation of many-color QCD as the functional (inhomogeneous) Laplace equation. We discretize the loop space by M-vertex polygons to approximate the functional laplacian by a (finite-dimensional) second order partial differential operator. A path-integral representation for the Green function of the functional laplacian is obtained as the M → ∞ limit of the Green function of the approximating operator. Finally, we speculate on the possibility of extending this approach to relativistic string.
ISSN:0370-2693
1873-2445
DOI:10.1016/0370-2693(88)90529-1