Improved Actions by Renormalization Group

重整化群的改进行动

• 批准号: 10640272
• 负责人: NAKAMURA Atsushi
• 金额: $ 1.92万
• 依托单位: Hiroshima University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640272/
• 关键词: QCD; Field Theory; Simulations; Renormalization group; Gluons; Improved action; ゲージ理論

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.

威尔逊提出格点规范理论，其中作用量由规范不变项组成。然而，行动的形式并不独特。到目前为止，最简单的一个已被用于数值模拟。通过引入其他项，我们可以改进模拟，即有机会获得更可靠、更接近连续统的结果。特别是作为重整化变换的结果出现的重整化轨迹上的动作，给出了没有晶格离散化伪影的“完美”结果。我们利用MonteCarlo重整化群分析得到了改进的作用量，利用Schwinger-Dyson方程研究了重整化群流。结果，我们发现了双耦合空间中重整化轨线的证据，并明确了它与Symanzik和Iwasaki作用量的关系。我们观察到重夸克势在到达重整化轨道时确实表现出更好的行为，并进一步找到了描述重整化流的有效β函数。由此我们可以得到数值模拟所需的基本参数，最终结果已发表在《核物理》上。

项目成果

S.Sakai,T.Saito and A.Nakamura: "ANISO TROPIC LATTICE WITH IMPROVED GAUGE ACTIONS.I. STUDY OF FUNDAMENTAL PARAMETERS IN WEAK COUPLING REGIONS"Nuclear Physics. B584. 528-542 (2000)

S.Sakai、T.Saito 和 A.Nakamura：“具有改进规范作用的ANISO TROPIC LATTICE.I.弱耦合区域基本参数的研究”核物理。

Ph.de Forcrand 他: "Effects of Chemical Potential on Hadron Masses at Finite Temperature"Nuclear Physics. B(PS)73. 477-479 (1999)

Ph.de Forcrand 等人：“有限温度下化学势对强子质量的影响”B(PS)73 (1999)。

F.Shoji,T.Suzuki,H.Kodama and A.Nakamura: "NEW GAUGE FIXING METHOD FOR ABELIAN PROJECTION"Physics Letters. B476. 199-204 (2000)

F.Shoji、T.Suzuki、H.Kodama 和 A.Nakamura：“阿贝尔投影的新规范固定方法”物理快报。

Ph.deForcrand 他: "MONTE CARLO RENORMALIZATION GROUP ANALYSIS OF QCD IN TWO-DIMENSIONAL COUPLING SPACE"Nuclear Physics. B(PS)83. 872-874 (2000)

Ph.deForcrand 等人：“二维耦合空间中 QCD 的蒙特卡罗重整群分析”核物理 B(PS)872-874。

QCDTARO Collaboration : Ph.deForcrand, A.Nakamura et al.: "Effects of Chemical Potential on Hadron Masses at Finite Temperature"Nucl.Phys.B. (Proc.Suppl.) 73. 477-479 (1999)

QCDTARO 合作：Ph.deForcrand、A.Nakamura 等人：“有限温度下化学势对强子质量的影响”Nucl.Phys.B。