Involution and Constrained Dynamics I: The Dirac Approach

Co-author(s): Robin W. Tucker

Reference: Journal of Physics A - Mathematical and General, 28 (1995) 4431-4451

Description: With this paper I returned to (well, mathematical) physics. It discusses the application of the formal theory of differential equations to constrained systems. We showed that the Dirac algorithm for finite-dimensional systems is just a special case of the general Cartan-Kuranishi completion procedure. But we also showed that this does not hold for field theories. There the (naive generalisation of the) Dirac algorithm is in general not sufficient to prove the consistency of a theory. We also presented an intrinsic method to count the degrees of freedom of a constrained system. However, the treatment of the finite-dimensional case contained an error (pointed out to me by Vladimir P. Gerdt). An improved and corrected treatment has been developed in the third part of this series [17] .

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