1987 Fiscal Year Final Research Report Summary
Quantum Theories of Gauge Fields and Anomalies, and their Applications
| Project/Area Number |
61540211
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
核・宇宙線・素粒子
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| Research Institution | HIROSHIMA UNIVERSITY |
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Principal Investigator |
KIMURA Toshiei Research Institute for Theoretical Physics, Hiroshima University, Professor, 理論物理学研究所, 教授 (30034606)
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| Co-Investigator(Kenkyū-buntansha) |
KUBO Reijiro Research Institute for Theoretical Physics, Hiroshima University,Associate Profe, 理論物理学研究所, 助教授 (60034609)
FUJIKAWA Kazuo Research Institute for Theoretical Physics, Hiroshima University,Professor, 理論物理学研究所, 教授 (30013436)
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| Project Period (FY) |
1986 – 1987
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| Keywords | Theory of elementary particles / Quantum theory of gauge fields / 場の量子論に現われる異常項 |
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| Research Abstract |
1. General theory of quantized field: Kimura gave a general procedure to obtain generatiors of gauge transformation in velocity phase space as well as in phase space. Kubo studied geometry, heat equation and Feynman's path integrals on the Poincare upper half-plane.
2. Anomalies: Using the path integral formulation, Fujikawa showed that, (1) Gauss law constraint in gauge theories may be derived directly. (2) Regularized BRS invariant measure of gravitational field is obtained. (3) The c-number term appeared in the Virasoro algebra is shown to relate directly with the anomaly. (4) In string theory with the conformal-type gauge fixing, the BRS symmetry is preserved even in the dimension D < 26, (5) Quantization of membrane is performed in a three-dimensional analogue of the conformal gauge. The chiral and gravitational anomalies are evaluated by Kimura and Yajima, when the torsion presents in addition to the gravitational field and the gauge fields. As a main result, it was shown that, in 6 dimensional space-time, the torsion does not affect the chiral anomaly and consistent gravitational anomaly, while the covariant gravitational anomaly survive owing to the torsion.
3. Application of field theory: Fujikawa showed that the nuclear collective rotation may be regarded as the analoge of Higgs mechanism. Kimura clarified, up to the post-post-Newtonian approximation, the relation of acceleration dependence of higher order gravitational potential of many body systems to the gauge of the gravitational field.
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