Improved Actions by Renormalization Group

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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.