BFT Embedding of Second-Class Systems

TL;DR

This paper explicitly constructs the variables of the first-class theory from second-class systems using BFT embedding and confirms their physical equivalence by comparing excitation spectra.

Contribution

It provides an explicit construction of first-class variables from second-class systems within the BFT embedding framework, extending the procedure beyond formal aspects.

Findings

Explicit variable construction for all cases

Demonstration of physical equivalence via spectra comparison

Extension of BFT embedding beyond formal level

Abstract

The embedding procedure of Batalin, Fradkin, and Tyutin, which allows to convert a second-class system into first-class, is pushed beyond the formal level. We explicitly construct, in all cases, the variables of the converted first-class theory in terms of those of the corresponding second-class one. Moreover, we only conclude about the equivalence between these two different kind of theories after compairing their respective spectra of excitations.