Master equations for extended Lagrangian BRST symmetries

Abstract

Starting from the requirement that a Lagrangian field theory be invariant under both Schwinger-Dyson BRST and Schwinger-Dyson anti-BRST symmetry, we derive the BRST-anti-BRST analogue of the Batalin-Vilkovisky formalism. This is done through standard Lagrangian gauge fixing respecting the extended BRST symmetry. The solutions of the resulting Master Equation and the gauge-fixing procedure for the quantum action can be brought into forms that coincide with those obtained earlier on algebraic grounds by Batalin, Lavrov and Tyutin.hepth@xxx/9302050

General triplectic quantization

“…in accordance with the conditions given in the previous section for any real constant β. Now we can introduce an extended quantum master equation 10) or equivalently,…”

“…F αa (φ * βb ). A general linear ansatz for F αa satisfying505 is then 10) which is nondegenerate on the 2N dimensional field manifold L 1 = {φ α }. One may notice that κ αβ in the symmetric V a of [5] and [1] satisfies κ αβ = −κ βα (−1) εαε β which implies ω αβ = 2κ αβ and that this antisymmetric κ αβ cannot be modified by the gradient shiftå16 since σ αβ inå17 is a symmetric matrix.…”

Superspace formulation for the Batalin-Vilkovisky formalism with extended BRST invariance

“…The vacuum functional is build up functionally integrating over all the fields involved in (13), represented here as µ α…”

Comments on the covariant Sp(2)-symmetric Lagrangian BRST formalism

“…It is interesting that even the "third set of fields" (φ A in the notation of [2]) have a completely natural place in the conventional Lagrangian BRST quantization scheme (without extended BRST symmetry). They are simple linear combinations of the collective fields that are needed to derive the Schwinger-Dyson BRST symmetry [5] through shifts φ A → φ A −ϕ A (where the fields ϕ A are linear combinations of the fieldsφ A that are required in the Sp(2)-symmetric formulation). In conventional Lagrangian BRST quantization one normally integrates these fields out of the path integral.…”

“…Just as ordinary Batalin-Vilkovisky Lagrangian quantization can be derived from the underlying principle of imposing the Schwinger-Dyson BRST symmetry [3] at all stages of the quantization procedure (and thus ensuring correct Schwinger-Dyson equations at the level of BRST Ward Identities) [4], the Sp(2)-symmetric scheme of ref. [2] can be derived from imposing the Sp(2)-symmetric version of the Schwinger-Dyson BRST symmetry [5]. See also the alternative derivation in [6].…”