Testing two versions of lattice gauge theory: Creutz ratios inU(1)3 |
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Authors: | Kevin Cahill Randolph Reeder |
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Institution: | (1) Department of Physics and Astronomy, University of New Mexico, 87131 Albuquerque, New Mexico;(2) Present address: AT-2, MS-H818, Los Alamos National Laboratory, 87545 Los Alamos, New Mexico |
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Abstract: | In our simplicial version of lattice gauge theory, we approximate Euclidean path integrals by tiling space-time with simplexes
and by linearly interpolating the fields throughout each simplex from their values at the vertices. We compare this method
with Wilson's lattice gauge theory forU(1) in three dimensions. As a standard of comparison, we compute the exact values of Creutz ratios of Wilson loops in the
continuum theory. Monte Carlo computations using the simplicial method give Creutz ratios within a few percent of the exact
values for reasonably sized loop atβ=1, 2, and 10. Similar computations using Wilson's method give ratios that typically differ from the exact values by factors
of 2 or more for 1⩽β⩽3.5 and that have the wrongβ dependence. The better accuracy of the simplicial method is due to its use of the action and domain of integration of the
exact theory, unaltered apart from the granularity of the simplicial lattice. We also present data on the action density and
the mass gap.
Research supported by the U.S. epartment of Energy under grant DE-FG04-84ER40166. |
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Keywords: | Lattice gauge theory simplex interpolation Wilson loops Creutz ratios U(1) Euclidean path integrals |
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