约束系统正则形式的对称性质

SYMMETRY IN CANONICAL FORMALISM OF CONSTRAINED SYSTEM

本文导出场论中用奇异拉氏量描述的系统正则形式的广义Noether第一定理(GNFT),导出无限连续群下变更性系统正则形式的广义Noether恒等式(GNI),讨论了它们在Dirac约束理论中的应用。给出一个新的反倒,说明Dirac猜想失效,指出某些变更性系统也具有Dirac约束,讨论了GNI在色动力学中的应用。

We have derived the generalized Noether's first theorem in canonical formalism for field theory with singular Lagrangian and generalized Noether's identities in canonical formalism for variant Lagrangian. The application to the Dirac's constraint theory was discussed. We point out that some variance system may has a Dirac constraint. A counter-example to a conjecture of Dirac was given which indicates that Dirac's conjecture is invalid in this example. The application of generalized Noether's identities to the chromodynamics is also discussed.