Constraints in Covariant Field Theories

Abstract

In this paper we have considered certain problems which arise when one attempts to cast a covariant field theory into a canonical form. Because of the invariance properties of the theory, certain identities exist between the canonical field variables. To insure that the canonical theory is equivalent to the underlying lagrangian formalism one must require that these identities, once satisfied, will remain satisfied through the course of time. In general, this will be true only if additional constraints are set between the canonical variables. We have shown that only a finite number of such constraints exist and that they form a function group. Our proof rests essentially on the possibility of constructing a generating function for an infinitesimal canonical transformation that is equivalent to an invariant infinitesimal transformation on the lagrangian formalism.