Perfect action on the lattice

本研究的目的是寻找格点规范作用量，使我们能够通过数值模拟对强相互作用基本粒子的物理性质作出精确的估计。这项研究的一个基本思想是找到一个不变的行动方面的规模变换。为此，我们在1995年和1996年用阻塞技术和Schwinger-Dyson方法研究了二维空间中的耦合流动和重整化轨道（1x 1和1x 2回路耦合），以确定重整化效应对耦合的影响。通过一系列的数值分析，揭示了耦合流动的总体特征和部分重整化轨迹。1997年，根据这些结果继续进行研究。为了考察截断效应对二维重整化轨迹的影响，在三维空间中进行了考虑扭环耦合的流动分析。结果表明，扭曲耦合的重正化效应是 ...更多信息 如果流动在2维重整化轨迹附近开始，则流动很小。这一结果表明，从计算成本的角度来看，二维重整化轨道附近的行动是足够的改进和实际有用的。研究了重整化轨道附近双圈耦合作用量的转动对称性恢复和物理量之比对晶格常数的弱依赖性。初步研究表明，与Symanzik作用量、Iwasaki作用量和Wilson作用量相比，该作用量具有更好的转动对称性恢复。至于弦张力与相变温度平方之比的依赖关系，它与岩崎的作用一样好。下一步将需要进行进一步的广泛检查。在研究过程中，开发了一个MPI（Message Passing Interface）规范场生成程序。它是为在现有的大规模并行计算机上进行大规模格点QCD模拟而设计的。少

Purpose of this investigation is to find lattice gauge actions which enable us to maake precise estimates for physical properties of strongly interacting elementary particles by numerical simulation. A basic idea for this investigation is to find a invariant action with respect to scale transformation. For this purpose, in 1995 and 1996, coupling flow and renormalized trajectory in 2-dmensional space (1x1 and 1x2 loop coupling) has been studied by blocking technique and Schwinger-Dyson method to determine renormalization effects to the couplings. As results of a series of numerical analysis, gross feature of coupling flow and a part of the renormalized trajectory has been clarified. In 1997, studies have been continued based on those results. In order to examine truncation effect on the 2-dimensional renormalization trajectory, flow analyzes have been made in 3-dimensional space where twist loop coupling has been included. It turned out that renormalization effect for twist coupling is … More small if flow starts near the 2-dimensional renormalization trajectory. This result has suggested that actions near the 2-dimensional renormalization trajectory is enough improved and practically useful one from a view point of computational cost. Restoration of rotational symmetry and week dependence of ratio of physical quantities on lattice constant were examined for the 2-loop coupling action near the renormalization trajectory. A preliminary study has indicated that the action shows much better restoration of rotational symmetry in comparison with Symanzik's action and Iwasaki's action as well as Wilson's one. As for the dependence of ratio between string tension and transition temperature squared, it is as good as Iwasaki's action. Further extensive examination will be required as the next step. A MPI (Message Passing Interface) program for gauge field generation on parallel processor has been developed in course of the investigation. It is designed for large scale lattice QCD simulation on currently available massively parallel computers. Less