Remarks on Constraint Analysis and Vacuum Persistence Amplitudes in Gauge Theories

In this work, we provide a general analysis of the subtleties of covariant quantum dynamics governing the interaction between matter and radiation, and present arguments that are useful for the quantization of arbitrary gauge models. Although the basic ingredients of constrained quantization are well established, we provide a compact and self-contained derivation that makes explicit the logical bridge between Dirac’s constraint formalism, Schwinger’s quantum action principle, and the Faddeev–Senjanovic construction of the transition amplitude and its functional measure structures, in a manner directly applicable to arbitrary electrodynamics models. As a direct application, not yet properly explored in the literature, we present the vacuum persistence amplitude of Stüeckelberg quantum electrodynamics in the regime where the Meissner effect arises.