Generalised Hamiltonian embedding of the Proca model

TL;DR

This paper transforms the Proca model into a gauge-invariant theory using the Batalin-Fradkin-Tyutin method, connecting it with St"uckelberg, Kalb-Ramond, and other models through gauge fields and path integrals.

Contribution

It introduces a generalized Hamiltonian embedding of the Proca model, revealing its relation to other gauge theories and models in a unified framework.

Findings

Embedded model's gauge-invariant fields match fundamental and observable fields.

Connection established between Proca, St"uckelberg, and Kalb-Ramond models.

Path integral approach clarifies model relationships.

Abstract

We convert the second class Proca model into a first class theory by using the generalised prescription of Batalin, Fradkin and Tyutin. We then show how a basic set of gauge invariant fields in the embedded model can be identified with the fundamental fields in the proca model as well as with the observables in the St\"uckelberg model or in the model involving the interaction of an abelian 2-form field with the Maxwell field. The connection of these models with the massive Kalb-Ramond model is also elucidated within a path integral approach.