Gauge symmetry in exact renormalization group

2014 Fiscal Year Final Research Report

• Project/Area Number: 22540270
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Particle/Nuclear/Cosmic ray/Astro physics
• Research Institution: Niigata University
• Principal Investigator: ITOH Katsumi 新潟大学, 人文社会・教育科学系, 教授 (50242392)
• Co-Investigator(Kenkyū-buntansha): IGARASHI Yuji 新潟大学, 人文社会・教育科学系, 名誉教授 (50151262)
• Co-Investigator(Renkei-kenkyūsha): SONODA Hidenori 神戸大学, 理学部, 准教授 (20291966)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 非摂動的場の理論 / 厳密くりこみ群 / ゲージ対称性を尊重する汎関数くりこみ群

Outline of Final Research Achievements

When we study a gauge theory in the exact renormalization group (ERG) method,
we encounter various problems owing to the fact that the momentum cutoff introduced is not compatible with the standard gauge symmetry. However, the symmetry survives in a modified form that depends on the regularization and its presence is expressed as the quantum master equation (QME) in the anti-field formalism. In the present project, the following results are obtained. 1) We showed that an anomaly, if it presents, appears as a breaking term in the QME. Related algebraic properties are also clarified. 2) The condition of QME can be solved partially to restrict the Wilson or the effective average action. RG flow equations are obtained for the actions that satisfy the condition. This is a novel way to treat the gauge symmetry in the ERG. In particular, the gauge two point function can be obtained explicitly in a full momentum dependent manner even in the presence of a finite cutoff.

Free Research Field

素粒子論