Noncompact Lattice Formulation of Gauge Theories

Details Noncompact Lattice Formulation of Gauge Theories Noncompact Lattice Formulation of Gauge Theories

1995-05-11

arxiv.org/abs/hep-lat/9505010v1

Phys.Rev. D52 (1995) 4053-4081

Physics

High Energy Physics

High Energy Physics - Lattice

72 pages, 3 Postscript figures

Scientific paper

10.1103/PhysRevD.52.4053

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 $\,\ell\,$.

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