The geometry of quantum gauge theories: A superspace formulation of BRST symmetry

Reducible gauge theories in local superfield Lagrangian BRST quantization

“…Additionally, the function S Ω L as 1 [1] (θ) is subject to the BFV-like condition of properness in the sense that rank 8) where the codimension of the surface Σ as 1 = {Γ P CL (θ)|Θâ 0 (θ) = 0} is calculated with respect to ΠT * M CL . The integrability of the HS in (3.8) is guaranteed by a double deformation of S Ω L as 1 [1] (θ): first in the powers of Φ * A k (θ) and then in the powers of Câ s (θ), in the framework of the existence theorem [3] for the classical master equation in the minimal sector, in the case of a purely topological theory (i.e., one without the potential term S 0 (A) = S (A(0), 0) in Sec.…”

“…The quantization rules [1] combine, in terms of superfields, a generalization of the "firstlevel" Batalin-Tyutin formalism [5] (the case of reducible hypergauges is examined in [6]) and a geometric realization of BRST transformations [7,8] in the particular case of θ-local superfield models (LSM) of Yang-Mills-type. The concept of an LSM [1,2,4], which realizes a trivial relation between the even t and odd θ components of the object χ = (t, θ) called supertime [9], unlike the nontrivial interrelation realized by the operator D = ∂ θ + θ∂ t in the Hamiltonian superfield N = 1 formalism [10] of the BFV quantization [11], provides the basis for the method of local quantization [1,2,4] and proves to be fruitful in solving a number problems that restrict the applicability of the functional superfield Lagrangian method [12] to specific gauge theories.…”

LAGRANGIAN Sp(3) BRST SYMMETRY FOR IRREDUCIBLE GAUGE THEORIES

“…On behalf of the relations (20) and (35)(36), we can write down the complete definitions of the three exterior longitudinal derivatives on the generators from the exterior longitudinal tricomplex in the context of the trigraduation governed by trideg, under the form…”

Gauge fixing in the Lagrangian formalism of superfield BRST quantization

“…Thus, in [1] a geometric representation of BRST transformations [7] in the form of supertranslations in superspace was realized; in [2,3] a superspace formulation of the action and BRST transformations for Yang-Mills theories was found; in [4] a superfield representation of the generating operator ∆ in the BV method was suggested; in [5] a closed superfield form of the BV quantization method [6] was obtained. In the study of [8], a multilevel generalization of the BV quantization formalism has been proposed, which ensures an invariant description of field-antifelds variables.…”

“…Recently, there has been a fairly large amount of papers [1,2,3,4,5] devoted to various superfield extensions of the BV quantization method [6] for gauge theories. Thus, in [1] a geometric representation of BRST transformations [7] in the form of supertranslations in superspace was realized; in [2,3] a superspace formulation of the action and BRST transformations for Yang-Mills theories was found; in [4] a superfield representation of the generating operator ∆ in the BV method was suggested; in [5] a closed superfield form of the BV quantization method [6] was obtained.…”