Transformation of second-class into first-class constraints in supersymmetric theories

TL;DR

This paper applies the BFFT method to supersymmetric quantum mechanics, converting second-class constraints into first-class ones while maintaining supersymmetry, which introduces additional restrictions.

Contribution

It extends the BFFT formalism to supersymmetric theories, ensuring the extended theory preserves supersymmetry with added auxiliary variables.

Findings

Successfully converts second-class to first-class constraints in supersymmetric models.

Maintains supersymmetry in the extended theory with auxiliary variables.

Identifies additional restrictions needed for supersymmetric consistency.

Abstract

We use the method due to Batalin, Fradkin, Fradkina, and Tyutin (BFFT) in order to convert second-class into first-class constraints for some quantum mechanics supersymmetric theories. The main point to be considered is that the extended theory, where new auxiliary variables are introduced, has to be supersymmetric too. This leads to some additional restrictions with respect the conventional use of the BFFT formalism.