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arXiv · hep-lat/9505010

Noncompact Lattice Formulation of Gauge Theories

R. Friedberg·T. D. Lee·Y. Pang·H. C. Ren
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Abstract

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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R. Friedberg, T. D. Lee, Y. Pang, H. C. Ren. 1995-05-11. Noncompact Lattice Formulation of Gauge Theories. https://doi.org/10.1103/physrevd.52.4053

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