标题： 非紧致格点规范理论的表述 显示英文标题

标题： Noncompact Lattice Formulation of Gauge Theories

摘要： 我们通过一个适当构造的完备布洛赫波函数集来展开规范场，每个布洛赫波函数由一个带标识$\,n\,$和一个限制在布里渊区内的波数$\,\vec K\,$标识。 通过仅限制展开到$\,0^{th}$带 ($\,n = 0\,$) 函数，可以推导出格点 QCD（或 QED）的一种非紧致表述，这些函数是与格点或链接上的离散值相关的简单连续插值。 通过包含所有$\,n = 0\,$和$\,n \ne 0\,$带可以达到精确的连续理论，而无需要求格点尺寸$\,\ell \to 0\,$。 这使得在非零$\,\ell\,$时，晶格耦合$\,g_\ell\,$可以作为重整化连续耦合起作用。当然，连续体中的所有物理结果都与$\,\ell\,$无关。 显示英文摘要

摘要： 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 $\,\ell\,$.