关于Dirac猜想的无效性

On the invalidity of Dirac's conjecture

对含第一类约束的系统,导出了该系统的正则Noether第一定理和正则Noether第二定理(扩展正则Noether恒等式).从正则Noether恒等式得到:与第一类约束相联系的Lagrange乘子(约束乘子)不是任意的.这对Dirac猜想的提出产生了疑问,给出的反例表明Dirac猜想无效就很自然了.

The canonical first Noether theorem and second Noether theorem(extended canonical Noether identities) in phase space for a system with firstclass constraints are formulated. Using the canonical Noether identities, it showns that the constraint multipliers connected with the firstclass constraints may not be arbitrary, this means that there is a question for putting forward a proposal given by Dirac. Thus the invalidity of Dirac's conjecture in the counterexamples is natural.