Non-Abelian BFFT embedding, Schrödinger quantization and the field–antifield anomaly of the O(N) nonlinear sigma model

Abstract

We embed the O(N ) nonlinear sigma model in a non-Abelian gauge theory. As a first class system, it is quantized using two different approaches: the functional Schrödinger method and the non-local field-antifield procedure. Firstly, the quantization is performed with the functional Schrödinger method, for N = 2, obtaining the wave functionals for the ground and excited states. In the second place, using the BV formalism we compute the one-loop anomaly. This important result shows that the classical gauge symmetries, appearing due to the conversion via BFFT method, are broken at the quantum level.

BRST Analysis and BFV Quantization of the Generalized Quantum Rigid Rotor

“…Particularities of the gauge choice become also more transparent through the proposed general perspective. The abelianization of some of these models has been studied in the literature, always on isolated terms, through different methods -for instance the BFFT conversion method has been recurrently applied to the nonlinear sigma model [41,61,62,67]. We hope that the general approach presented here may consolidate further treatments of these similar systems in a unified way.…”

“…The use of auxiliary variables to promote the abelianization of the second-class constraints has been summarized in the Batalin-Fradkin-Fradkina-Tyutin (BFFT) method [29,30,31,32], of which some important applications can be seen in [33,34,35,36]. Since then, there has appeared many generalizations of the BFFT ideas, we mention for instance the improved BFFT [37,38], the embedding BFFT [39,40,41], the Wotsazek-Neves [42,43] and the gauge-unfixing methods [44,45,46,47,48]. The very interpretation of some of the second-class constraints as gauge-fixing conditions for other corresponding constraints, which then acquire the status of first-class ones, has also produced an interesting investigative analysis [49,50,51].…”

BFFT Nonlinear Constraints Abelianization of a Prototypical Second-Class System

“…α of the form (42) with coefficients (47). A corresponding statement holds for the existence of a simple involutive Hamiltonian in the form (48) satisfying…”

“…In reference [37], we can see the use of BFFT variables in a constraints conversional approach to discuss the quantization of the anomalous chiral Schwinger model. It is also worth mentioning here the appearance of many extensions and generalizations of the original BFFT formalism such as the improved BFFT [38,39], the embedding BFFT [40,41,42], the Wotsazek-Neves [43,44] and the gauge-unfixing [45,46,47,48,49] methods. Since the BFFT general solution, resulting from the analysis of references [4,5,6,7,8], comes as a power series in the auxiliary variables, the question of obtaining closed expressions for the converted constraints poses itself as a natural one.…”