Anomalies in Gauge Theories and Related Phenomena

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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 Grant-in-Aid over the past two-year 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 condensed-matter physics from the viewpointof gauge-field 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) Charge-density waves (CDW) : We have studied symmetry-related features of the CDW transport phenomenon in one-dimensional 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 Kac-Moody algebra arises in the long-wavelength structure of one-dimensional electron-phonon 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 quasi-particles obeying fractional statistics (anyons) in connection with high-temperature superconductivity. We have studied anyons within the framework of 3-dimensional gauge theories and shown that fractional statistics realized for widely-separated anyons disappears when anyons come close to each other.(3) Quantum Hall Effect : We have constructed a collective-field theory which describes electrons in a magnetic field in terms of a multi-component 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