Anomalies in Gauge Theories and Related Phenomena
Project/Area Number  01540249 
Research Category 
GrantinAid for General Scientific Research (C)

Allocation Type  Singleyear Grants 
Research Field 
核・宇宙線・素粒子

Research Institution  Osaka University 
Principal Investigator 
SHIZUYA Kenichi Osaka University, Department of Physics Associate Professor, 理学部, 助教授 (50154216)

Project Period (FY) 
1989 – 1990

Project Status 
Completed(Fiscal Year 1990)

Budget Amount *help 
¥2,400,000 (Direct Cost : ¥2,400,000)
Fiscal Year 1990 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1989 : ¥1,600,000 (Direct Cost : ¥1,600,000)

Keywords  Anomalies / Chiral symmetry / Gauge theories / Charge density waves / Anyons / KacMoody algebra / Quantum Hall effect / HighT superconductivity / 端数粒子統計 
Research Abstract 
Symmetries play an important role in physics. Classical symmetries, however, sometimes fail to survive quantization ; and their quantum modifications are called anomalies. Anomalies thus represent some deep structures of quantum nature and often serve as a key in understanding physical phenomena of traly quantum nature. In view of this, under the GrantinAid over the past twoyear period, we have (1) pursued consistent quantization of anomalous gauge theories to clarify the roles of anomalies, and (2) have investigated quantum transport phenomena in condensedmatter physics from the viewpointof gaugefield theories. 1. We have examined the consistency and current algebras of anomalous gauge theories two and four dimensions. This work was done in collaboration with Dr. S. Miyake at Tohoku University. 2. (1) Chargedensity waves (CDW) : We have studied symmetryrelated features of the CDW transport phenomenon in onedimensional conductors in terms of its underlying chiral symmetry and chi
… More
ral anomaly. In particular, it is Pointed out that a local chiral symmetry based on the KacMoody algebra arises in the longwavelength structure of onedimensional electronphonon systems ; and the CDW are identified with massless modes associated with this local symmetry. This work was done in collaboration with Prof. B. Sakita at the City College of New York (CCNY). (2) Anyons : There has recently been considerable interest in quasiparticles obeying fractional statistics (anyons) in connection with hightemperature superconductivity. We have studied anyons within the framework of 3dimensional gauge theories and shown that fractional statistics realized for widelyseparated anyons disappears when anyons come close to each other. (3) Quantum Hall Effect : We have constructed a collectivefield theory which describes electrons in a magnetic field in terms of a multicomponent Dirac field in (1+1) dimensions, and studied quantization of the Hall conductance in relation to Berry's phase. A paper is now in preparation. Less

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