Involution and Constrained Dynamics III

Intrinsic Degrees of Freedom Count

Abstract

The formal theory of differential equations is applied to constrained dynamics in order to give an intrinsic definition of the number of degrees of freedom of a mechanical system or a field theory. We show how the action of a gauge (pseudo) group can be easily taken into account by some purely formal and combinatorial calculations. As a by-product we exhibit the connection between the Hilbert functions of two difierential equations related by a differential relation.