Applying Constraints from Outside the System

We investigate the role of external constraints in quantum field theory using the path integral formalism. We begin by reviewing the quantization of constrained systems and extend the analysis to cases where constraints are added to the action via auxiliary fields. These constraints involve both the degrees of freedom and their time derivatives. Using the resulting framework, we derive the generating functional for matter vector fields constrained to the spin-one state. However, for systems with singular actions, preserving the classical form of constraints at the quantum level requires conditions, and we provide examples of sufficient conditions. We also present an example where the classical form of constraints is not preserved, involving a singular action with an antisymmetric tensor field leading to a strength-field interpretation.