Topologically Massive Abelian Gauge Theory From BFT Hamiltonian Embedding of A First-order Theory

TL;DR

This paper demonstrates how a new first-order gauge non-invariant massive spin-one theory can be embedded into a gauge-invariant abelian B∧F theory using the BFT Hamiltonian embedding, establishing their equivalence.

Contribution

It introduces a novel first-order formulation of massive spin-one theory and shows its equivalence to a topologically massive gauge theory via Hamiltonian embedding.

Findings

The embedded Hamiltonian reproduces the equations of motion of the original theory.

Both theories are shown to be equivalent through phase space partition functions.

The approach provides a new perspective on massive spin-one theories and their gauge invariance.

Abstract

We start with a new first order gauge non-invariant formulation of massive spin-one theory and map it to a reducible gauge theory viz; abelian $B{\wedge}F$ theory by the Hamiltonian embedding procedure of Batalin, Fradkin and Tyutin(BFT). This equivalence is shown from the equations of motion of the embedded Hamiltonian. We also demonstrate that the original gauge non-invariant model and the topologically massive gauge theory can both be obtained by suitable choice of gauges, from the phase space partition function of the emebedded Hamiltonian, proving their equivalence. Comparison of the first order formulation with the other known massive spin-one theories is also discussed.