GEOMETRIC APPROACH TO QUANTUM ANOMALIES.

量子异常的几何方法。

• 批准号: 63540229
• 负责人: KITAKADO Shinsaku
• 金额: $ 0.51万
• 依托单位: Toyota Technological Institute
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1988
• 资助国家: 日本
• 起止时间: 1988 至 1989
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-63540229/
• 关键词: quantum anomaly; Wess-Zumino model; BRST-quantization; Chern-Simons term; topological field theory; anomalous commutator; 位相幾何学的場の理論; BRST-量子化; BFVの量子化法; グラスマン数; 統計性; BRST; 拘束系; Second Class Constraint.

Anomalous gauge theories considered as constrained systems are investigated. The effects of chiral anomaly on the canonical structure are examined first for nonlinear sigma-model and later for fermionic theory. The breakdown of Gauss law constraints and the anomalous commutators among them are studied in a systematic way.An intrinsic mass term for gauge fields makes it possible to solve the Gauss law relations as second class constraints and to quantize the system A la Dirac. Based upon the Ward-Takahashi identities for gauge symmetry, we investigate anomalous fermionic theory within the framework of path integral approach.As a second topic, we have BRST-quantized the topological Yang-Mills theory in four dimensions and the topological sigma-model in two dimensions, using the generalized Hamiltonian formalism developed by Batalin, Fradkin and Vilkovisky.

研究了被视为约束系统的反常规范理论。首先针对非线性西格玛模型检查手性反常对正则结构的影响，然后针对费米子理论进行检查。系统地研究了高斯定律约束的分解以及其中的反常换向子。规范场的内在质量项使得将高斯定律关系作为二类约束求解并量化系统A la Dirac成为可能。基于规范对称性的 Ward-Takahashi 恒等式，我们在路径积分方法的框架内研究了反常费米子理论。作为第二个主题，我们对四维拓扑 Yang-Mills 理论和拓扑 sigma 模型进行了 BRST 量化。二维，使用由巴塔林、弗拉德金和维尔科维斯基开发的广义哈密顿形式主义。

项目成果

T. Fujiwara, and S. Kitakado: "Anomalous Gauge Theories as Constrained Hamiltonian Systems" Zeitschrift fur Physik C Vol.43, pp.201-214, 1989.

T. Fujiwara 和 S. Kitakado：“作为约束哈密顿系统的反常规范理论”Zeitschrift Fur Physik C Vol.43，第 201-214 页，1989 年。

T.Fujiwara,;S.Hosono,;S.Kitakado.: Modern Physics Letters A. 3(16). 1585-1594 (1988)

T.Fujiwara,;S.Hosono,;S.Kitakado.：现代物理学快报 A. 3(16)。

T.Fujiwara,S.Hosono and S.Kitakado: "Chirally Gauged Wess-Zumino-Witten Model as a Constrained System" Modern Physics Letters A. 3(16). 1585-1594 (1988)

T.Fujiwara、S.Hosono 和 S.Kitakado：“作为约束系统的手性测量 Wess-Zumino-Witten 模型”《现代物理学快报》A. 3(16)。

Y.Ohnuki: "Unitary Representations of the Poincare Group and Relativistic Wave Equations" World Scientific Pub., 213 (1988)

Y.Ohnuki：“庞加莱群和相对论波动方程的酉表示”世界科学出版社，213（1988）

Y.Igarashi,H.Imai,S.Kitakado and H.So: "Hamiltonian BRST Quantization of Topological Field Theories" Physics Letters B. 227(2). 239-244 (1989)

Y.Igarashi、H.Imai、S.Kitakado 和 H.So：“拓扑场论的哈密尔顿 BRST 量子化”《物理快报》B. 227(2)。