场论中高阶微商规范系统的量子对称性质  

The quantum symmetries in field theories for a gauge-invariant system with a higher-order Lagrangian

作　　者：李子平[1] 

机构地区：[1]北京工业大学应用数理学院

出　　处：《商丘师范学院学报》2007年第3期5-12,共8页Journal of Shangqiu Normal University

基　　金：国家自然科学基金(19275009)资助项目;北京市自然科学基金(1942005)资助项目

摘　　要：基于高阶微商规范系统Green函数的生成泛函,导出了该系统在量子水平下的变换性质方程,给出了系统存在量子守恒律的条件和守恒量的表达式.用于高阶微商非Abel Chern-Simons理论,求出了系统的量子BRST守恒荷和其他守恒荷;讨论共形变换下量子水平的变换性质,导出了系统的量子守恒角动量,指出该系统在量子理论中仍可保持分数自旋性质,但经典对称性和守恒律的联系在量子水平不一定再保持.Based on the generating functional of the Green functions for the gauge - invariant system in higher-order derivatives field theories, the equations of the transformation properties at the quantum level have been derived. It follows that the sufficient condition which implies that there exists the quantal conservation laws, and the expressions of the quantal conserved laws are also given. Applying the results to the higher-order derivatives non-Abelian Chern-Simons theories, the quantal BRST conserved charge and other conserved charges are found, the transformation properties of the conformal transformation at the quantum level are discussed, the quantal conserved angular momentum is derived, it pointed out that fractional spin in this system may be also preserved in quamtum theories. But the connection between the symmetries and conservation laws in classical theories are not always preserved in quantum theories.

关 键 词：高阶微商理论 规范场 路径积分量子化 对称性和守恒律 Chern—Simons理论 

分 类 号：O413.3[理学—理论物理]