Hamiltonian vs Lagrangian Embedding of a Massive Spin-one Theory Involving 2-form Field

TL;DR

This paper compares Hamiltonian and Lagrangian embeddings of a massive spin-one gauge theory with an antisymmetric tensor field, highlighting differences in their constraint structures and gauge reducibility.

Contribution

It applies the BFV-BRST approach to embed the model into a first class system and analyzes the contrasting features of the embedded Hamiltonian and Lagrangian formulations.

Findings

The embedded Hamiltonian and Lagrangian models have distinct constraint structures.

Manifestly covariant St"uckelberg Lagrangian requires further phase space enlargement.

Reducible gauge structure naturally emerges in the embedded model.

Abstract

We consider the Hamiltonian and Lagrangian embedding of a first-order, massive spin-one, gauge non-invariant theory involving anti-symmetric tensor field. We apply the BFV-BRST generalised canonical approach to convert the model to a first class system and construct nil-potent BFV-BRST charge and an unitarising Hamiltonian. The canonical analysis of the St\"uckelberg formulation of this model is presented. We bring out the contrasting feature in the constraint structure, specifically with respect to the reducibility aspect, of the Hamiltonian and the Lagrangian embedded model. We show that to obtain manifestly covariant St\"uckelberg Lagrangian from the BFV embedded Hamiltonian, phase space has to be further enlarged and show how the reducible gauge structure emerges in the embedded model.