Gauge fixing in the Lagrangian formalism of superfield BRST quantization

Abstract

We propose a modification of the gauge-fixing procedure in the Lagrangian method of superfield BRST quantization for general gauge theories, which simultaneously provides a natural generalization of the well-known BV quantization scheme as far as gauge-fixing is concerned. A superfield form of BRST symmetry for the vacuum functional is found. The gauge-independence of the S-matrix is established.

The effective action for superfield Lagrangian quantization in reducible hypergauges

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[3][4][5]. The superfield quantization [3], which is applicable in the canonical formalism and in its implication -Lagrangian formalism, makes use of the nontrivial relation of the odd Grassmann η and even t projections of supertime, Γ = (t, η), as distinct from the Lagrangian quantization [4,5].

Note that algorithmic methods have been found [6] for constructing generalized Poisson sigma models in the framework of the superfield formalism [7].

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“…The superfield quantization [3], which is applicable in the canonical formalism and in its implication -Lagrangian formalism, makes use of the nontrivial relation of the odd Grassmann η and even t projections of supertime, Γ = (t, η), as distinct from the Lagrangian quantization [4,5].…”

“…In the SLQ, we realize the explicit superfield representation of the structural functions of a gauge algebra (GA), not indicated in [4,5], in the framework of an η-local superfield model (SM) which includes the initial standard gauge model.…”

“…In this paper, we describe the Lagrangian and Hamiltonian formulations of the SM, specify quantization rules, and determine, based on the component formulation, the relations of the proposed quantization scheme to the superfield quantization [4,5] and multilevel formalism [9].…”

“…We make use of some of conventions from [4,5] and the condensed notation from [10]. The rank of an even supermatrix is characterized by a pair of numbers (k + , k ─ ), where k + and k ─ are the respective ranks of the Bose-Bose and Fermi-Fermi blocks of the supermatrix with respect to the basic Grassmann parity ε.…”