Hamilton动力系统的对称性质

Symmetry Properties of Hamiltonian Dynamical System

分别就场论中正则拉氏量和奇异拉氏量描述的系统导出了相空间中的广义Noether第一定理(GFNT)和守恒律及规范变更系统相空间中的广义Noether恒等式(GNI),得到了系统的强守恒律和弱守恒律。Dirac猜想有效时,沿约束系统运动的轨线,相空间中的GNI可给出与第一类约束相联系的拉氏乘子所满足的关系,将GNI用于杨-Mill场,即得到了与次级第一类约束相联系的拉氏乘子(不含微商)所适合的关系。约束的相容性条件不能由规范不变的性质导出,该条件不是强成立的,Dirac-Bergmann程序在弱成立下才是自洽的。

We derive generalized first Noether's theorem for regular and singular Lagrangian system respectively, the dynamics of which is described by Hamilton's canonical variables, derive generalized Noeth-er's identities for gauge-variant system in phase space, and deduce the strong and weak conservation laws for constrained Hamiltonian system in phase space. If Dirac conjecture is valid, along the trajectory of motion of constrained system, we obtain some relationship of Lagrangian multipliers in connection with secondary first class constraints. A preliminary application to Yang-Mill fields was given. The consistancy conditions of constraints can not be deduced from the properties of the gauge invariance, such consistency conditions do not hold in the strong validity sense. Dirac-Beramann's algorithm is consistent in the sense of weak validity.