格点朗道规范的球极投影法
Lattice Landau gauge via Stereographic Projection
摘要：
在修正格点朗道规范中，格点BRST的Gribov拷贝完全取消和Neuberger 0/0问题都可以避免。在紧致U（1）中，问题是一个晶格伪影，仍然存在Gribov副本，但它们的数量呈指数级减少。此外，由于Faddeev-Popov行列式的符号是正的，所以那里没有副本的取消。应用于极大阿贝尔子群，这也避免了SU（N）的剩余Gribov副本之间的完美抵消。此外，基于格点上的规范场作为立体投影链接变量的定义，它提供了规范固定蒙特卡罗模拟的框架。这将包括所有Gribov副本在BRST的精神。它们的平均值不是零，正如简单模型中明确证明的那样。这可能解决目前规范固定格点和QCD格林函数连续研究之间的矛盾。
英文摘要：
The complete cancellation of Gribov copies and the Neuberger 0/0 problem of lattice BRST can be avoided in modified lattice Landau gauge. In compact U(1), where the problem is a lattice artifact, there remain to be Gribov copies but their number is exponentially reduced. Moreover, there is no cancellation of copies there as the sign of the Faddeev-Popov determinant is positive. Applied to the maximal Abelian subgroup this avoids the perfect cancellation amongst the remaining Gribov copies for SU(N) also. In addition, based on a definition of gauge fields on the lattice as stereographically-projected link variables, it provides a framework for gauge fixed Monte-Carlo simulations. This will include all Gribov copies in the spirit of BRST. Their average is not zero, as demonstrated explicitly in simple models. This might resolve present discrepancies between gauge-fixed lattice and continuum studies of QCD Green's functions.
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