Improved Actions by Renormalization Group

威尔逊提出了格点规范理论，其中作用量是由规范不变项组成的。然而，诉讼的形式并不是独一无二的。到目前为止，最简单的方法已经用于数值模拟。通过引入其他项，我们可以改进模拟，即我们有机会得到更可靠的结果，更接近于连续介质的结果。特别是作为重整化变换结果的重整化轨迹上的作用量，给出了不受晶格离散化伪影影响的“完美”结果。我们通过蒙特卡罗重整化群分析得到了改进的作用量。我们用Schwinger-Dyson方程研究了重整化群流。结果，我们在二耦合空间中发现了重整化轨道的证据，并且与Symanzik和Iwaaki作用量的关系也变得清晰起来。我们观察到重夸克势在达到重整化轨道时确实表现出了更好的行为。我们进一步找到了描述重整化流动的有效的β函数。由此我们可以得到我们在数值模拟中所需要的基本参数。我们已经在《核物理》上发表了最终结果。

Wilson proposed the lattice gauge theory where actions are consists of gauge invariant terms. The form of the actions, however, is not unique. So far the simplest one has been used for numerical simulations. By introducing other terms, we can improved simulations, i.e, we have chance to get more reliable results which are closer to the continuum ones. Especially actions on the renormalized trajectory, which appears as the result of the renormalization transformation, give "perfect" results which are free from lattice discretization artefact. We have performed to get the improved actions by Monte Carlo renormalization group analysis.We have employed Schwinger-Dyson equation and investigated the renormalization group flow. As the result, we have found the evidence of the renormalized trajectory in the two-coupling space, and the relation to Symanzik and Iwasaki actions has become clear. We have observed that the heavy quark potential shows indeed the better behavior when reaching to the renormalized trajectory.We have further found an effective beta function which describes the renormalization flow. From this we can obtain fundamental parameters which we need in numerical simulations.We have published the final results in Nuclear Physics.