Extension of the Dirac-Bergmann theory of constrained systems

According to Dirac’s and Bergmann’s physical ideas, we derive the expression of the finite Dirac contact transformation, propose an extended Dirac conjecture, extend Dirac’s original consistency conditions, and obtain the correct definition of physical observables as well as more universal gauge conditions in general singular Lagrangian systems. The difficulties in Cawley’s first and second counterexamples of Dirac’s conjecture are overcome. Our results are applicable to Hamiltonization of systems with Hessian variable rank and systems with the proper subalgebra of the minimum evolution closed Poisson bracket of first-class constraints, and so provide a correct tool for quantization of these systems. © 1996 The American Physical Society.