非紧致规范理论在格点上的更大物理体积及物质场数目界限
Larger physical volume and bounds on the number of matter fields in noncompact gauge theories on a lattice
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中文总结 AI 辅助
本文通过微扰计算确认非紧致格点正则化可提供更大物理体积，发现有效间距比R最大为sqrt(2)，并给出物质场中标量与旋量自由度数目之差的界限。
中文摘要 AI 辅助
这项工作源于数值结果：在纯SU(2)规范理论中，有效非紧致与紧致格点间距之比R大于1，并随规范耦合减小而增大，同时预期在扩展参数空间后该比值会进一步增加。这意味着采用非紧致正则化时，在给定格点数和可比较的标度下，可以获得更大的物理体积，而其对尺寸效应控制的重要性早已为人所知。我们通过非紧致纯SU(2)和阿贝尔规范理论中普朗克常数展开的有效格点间距的微扰计算，定性确认了上述结果和预期，但此外发现R达到最大值sqrt(2)。在包含物质场时，我们发现R增大（仍不超过sqrt(2)）或减小，取决于标量与旋量自由度数目之差，且该差值存在界限。
英文摘要
The work was motivated by the numerical result that in a pure SU(2) gauge theory the ratio R of the effective non-compact and compact lattice spacing is larger than 1 and increasing with decreasing gauge coupling, as well as the expectation that it should further increase extending the parameter space. This means that with a noncompact regularization, at given number of lattice sites and comparable scaling, one can obtain a larger physical volume, whose importance for the control of size effects has long been known. We confirm qualitatively results and expectation by a perturbative evaluation of the effective lattice spacing in an expansion in the Plank constant of non-compact pure SU(2) and Abelian gauge theories, but we find in addition that R reaches the maximum value of sqrt(2). Including matter fields we find that R increases ( still up to sqrt(2) ) or decreases depending on the difference between the number of scalar and spinor degrees of freedom, and there are bounds on such a difference.
发表机构
- INFN, Laboratori Nazionali di Frascati（意大利国家核物理研究所，弗拉斯卡蒂国家实验室）
机构由 AI 辅助整理，请以论文原文为准。
