BFFT quantization with nonlinear constraints

TL;DR

This paper analyzes the BFFT method for converting second-class to first-class constraints in nonlinear theories, highlighting its limitations and proposing potential solutions.

Contribution

It provides a detailed analysis of the BFFT method's applicability to nonlinear theories and discusses the impracticality of certain simplifications.

Findings

Simplification conditions for BFFT in nonlinear theories are identified.

Full BFFT method often necessary due to impracticality of simplifications.

Potential solutions for overcoming limitations are proposed.

Abstract

We consider the method due to Batalin, Fradkin, Fradkina, and Tyutin (BFFT) that makes the conversion of second-class constraints into first-class ones for the case of nonlinear theories. We first present a general analysis of an attempt to simplify the method, showing the conditions that must be fulfilled in order to have first-class constraints for nonlinear theories but that are linear in the auxiliary variables. There are cases where this simplification cannot be done and the full BFFT method has to be used. However, in the way the method is formulated, we show with details that it is not practicable to be done. Finally, we speculate on a solution for these problems.