On generalized gauge fixing in the field–antifield formalism

Abstract

We consider the problem of covariant gauge-fixing in the most general setting of the fieldantifield formalism, where the action W and the gauge-fixing part X enter symmetrically and both satisfy the Quantum Master Equation. Analogous to the gauge-generating algebra of the action W , we analyze the possibility of having a reducible gauge-fixing algebra of X. We treat a reducible gauge-fixing algebra of the so-called first-stage in full detail and generalize to arbitrary stages. The associated "square root" measure contributions are worked out from first principles, with or without the presence of antisymplectic second-class constraints. Finally, we consider an W -X alternating multi-level generalization.

Semidensities, second-class constraints, and conversion in anti-Poisson geometry

“…However, the dependence is so soft that physics, which lives on-shell, is not affected [8]. We shall here clarify in exactly what sense the ∆ E D operator remains invariant on-shell under reparametrization of the constraints.…”

“…In Darboux coordinates Γ A , the ∆ E operator is defined on a semidensity σ as [8,10,11,12,13] ( [13] and in the degenerate case in Ref. [8].…”

“…[8] was that one cannot maintain a strong nilpotency of the Dirac odd Laplacian ∆ ρ,E D under reparametrization of the second-class constraints. This is consistent with our new results.…”

Reducible gauge theories in local superfield Lagrangian BRST quantization

“…The definitions in Eqs. (2.55)-(2.58) generalize, to the case of reducible mixed antisymplectic constraints in the context of a dynamical LSM, the formal definition [6,23] of irreducible second-class antisymplectic constraints for θ = 0 .…”

“…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.…”