Hamilton-Jacobi and Schrödinger Theory in Theories with First-Class Hamiltonian Constraints

Brief proofs are given, applying in the case of classical Hamilton-Jacobi theory to the action $S$, and in a Schrödinger-type quantum theory to the state vector $\Psi$, (1) that these quantities are independent of the time $t$, and (2) that they as well as the equations obeyed by them are form-invariant under the invariance group of transformations, provided the invariance transformations are generated by constraints and provided these constraints include the Hamiltonian. In Dirac's version the equations of general relativity have all these properties.