Constraints in Covariant Field Theories. II

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Abstract
In this paper we analyze the difficulties which occur when one attempts to quantize a theory such as electrodynamics or the general theory of relativity. Because of the invariance properties of theories of this type all of the canonical variables of the theory are not independent of one another but rather there exists certain algebraic relations between them called constraints. These constraints plus the Hamiltonian, in the unquantized version of the theory, constitute a function group. It is proved that there exists at least one ordering of factors in the quantized theory for which this is also true. From this fact we conclude that it is possible, at least formally, to construct a quantum version of the theories under consideration and that the quantum version will possess the same invariance properties as the corresponding unquantized theory.

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