Superfield quantization

Abstract

We present a superfield formulation of the quantization program for theories with first class constraints. An exact operator formulation is given, and we show how to set up a phase-space path integral entirely in terms of superfields. BRST transformations and canonical transformations enter on equal footing, and they allow us to establish a superspace analog of the BFV theorem. We also present a formal derivation of the Lagrangian superfield analogue of the field-antifield formalism, by an integration over half of the phase-space variables.

Hamiltonian superfield formalism with N supercharges

“…[1,2]. Here we review the N = 1 path integral construction, as it serves as an important prototype for further developments.…”

Reducible gauge theories in local superfield Lagrangian BRST quantization

“…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. The idea of an LSM makes it possible to obtain an odd-Lagrangian and odd-Hamiltonian form of the classical master equation as a condition that preserves a θ-local analogue of the energy by virtue of Noether's first theorem with respect to the evolution along the variable θ, defined by superfield extensions of the extremals for an initial gauge model, i.e., by odd-Lagrangian (LS) and oddHamiltonian (HS) systems.…”

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].…”

“…The quantization described in [3] has been generalized for two and more supersymmetries which are associated with Grassmann variables…”