Gauge fixing procedure in the extended BRST theory. The example of the abelian 2-forms

Abstract

The paper proposes a general procedure to find the form of the gauge fixing term in the extended BRST quantization of the gauge theories, a difficult problem in the standard approach. Our proposal is based on the many level structure of the extended spaces and leads to a simple form of the gauge fixing term. The abelian 2-form model is completely analyzed as an example.

A Chern–Simons gauge-fixed Lagrangian in a ‘non-canonical’ BRST approach

“…By this, a simple gauge-fixing term of the form (28) can be transferred using some non-canonical variables. All these facts are presented by many authors, as for example in [17] for the standard theory and in [11] for the sp(2) formalism. We will develop here the equivalence between the Hamiltonian and the Lagrangian formalism at the level of the sp(2) approach, particularly applied for the model given by ( 4).…”

“…On the other hand, the sp(2) BRST Hamiltonian formalism is easier to be implemented, there are clearly defined rules for choosing an adequate ghost spectrum and there is a simple gauge-fixing procedure [11], non-applicable in the pure Lagrangian approach. Moreover, the use of the sp(2) Hamiltonian formalism offers a great advantage in the quantum approach, especially in the case of open groups [12].…”

From the Hamiltonian to the Lagrangean formalism for 1-reducible theories. The Freedman-Townsend model

“…Special constructions when the BRST operator s can be split in many anticommuting pieces have been proposed-the sp(2) case [13] and the sp(3) case [5,7]. In this last case,…”

“…The importance of our approach consists in the fact that it will allow the explanation of the form of the master equations in the Lagrangean case, an explanation not at all clear in a direct Lagrangean construction. Although it is not tackled here, the gauge fixing problem is also clearly solved on the basis of the equivalence [5].…”

The generalized semidiscrete cmKdV system and the periodic reduction

“…The complete integrability of dynamical systems represent a topic of interest for the field of nonlinear science. There are several criteria and techniques for investigating integrability such as: complexity growth [1], singularity confinement [2], cube consistency [3], Lax representation [4][5][6], Lie symmetry approach [7,8] and the Hirota bilinear and super-bilinear formalism [9][10][11][12]. For constrained systems and gauge theories, the Becchi-Rouet-Stora-Tyutin (BRST) technique [13][14][15][16] can be applied.…”