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Noncompact Lattice Formulation of Gauge Theories

By R. Friedberg, T. D. Lee, Y. Pang and H. C. Ren


We expand the gauge field in terms of a suitably constructed complete set of Bloch wave functions, each labeled by a band designation $\,n\,$ and a wave number $\,\vec K\,$ restricted to the Brillouin zone. A noncompact formulation of lattice QCD (or QED) can be derived by restricting the expansion only to the $\,0^{th}$-band ($\,n = 0\,$) functions, which are simple continuum interpolations of discrete values associated with sites or links on a lattice. The exact continuum theory can be reached through the inclusion of all $\,n = 0\,$ and $\,n \ne 0\,$ bands, without requiring the lattice size $\,\ell \to 0\,$. This makes it possible, at a nonzero $\,\ell\,$, for the lattice coupling $\,g_\ell\,$ to act as the renormalized continuum coupling. All physical results in the continuum are, of course, independent of $\,\ell\,$.Comment: 72 pages, 3 Postscript figure

Topics: High Energy Physics - Lattice
Publisher: 'American Physical Society (APS)'
Year: 1995
DOI identifier: 10.1103/PhysRevD.52.4053
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