On Possible Generalizations of Field-Antifield Formalism

Abstract

A generalized version is proposed for the field-antifield formalism. The antibracket operation is defined in arbitrary field-antifield coordinates. The antisymplectic definitions are given for first-and second-class constraints. In the case of second-class constraints the Dirac's antibracket operation is defined. The quantum master equation as well as the hypergauge fixing procedure are formulated in a coordinate-invariant way. The general hypergauge functions are shown to be antisymplectic first-class constraints whose Jacobian matrix determinant is constant on the constraint surface. The BRST-type generalized transformations are defined and the functional integral is shown to be independent of the hypergauge variations admitted. In the case of reduced phase space the Dirac's antibrackets are used instead of the ordinary ones. †

Gauge fixing in the Lagrangian formalism of superfield BRST quantization

“…At the same time, in the present approach the gauge-independence is encoded in BRST transformations controlled by generating equations imposed on the entire gauge part of the quantum action, whereas in the framework of [8] this role is played by unimoduar involution relations imposed on hypergauge functions. Despite the formal similarity between the vacuum functional (32) proposed by the present study and the ansatz (33) suggested by [8] the two methods appear to be independent from each other, being different generalizations of the BV method.…”

“…At the same time, in the present approach the gauge-independence is encoded in BRST transformations controlled by generating equations imposed on the entire gauge part of the quantum action, whereas in the framework of [8] this role is played by unimoduar involution relations imposed on hypergauge functions. Despite the formal similarity between the vacuum functional (32) proposed by the present study and the ansatz (33) suggested by [8] the two methods appear to be independent from each other, being different generalizations of the BV method. However, as is seen from the above comparison, the vacuum functional (32) proposed by the present study becomes identical, in the particular case of linear dependence on the Lagrange multipliers, with the first-level vacuum functional [8] considered in the case of a trivial integration measure and vanishing structure functions.…”

“…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.…”

“…On the one hand, this approach to gauge-fixing guarantees the independence of the vacuum functional (and, hence, that of the S-matrix) from any particular choice of the gauge. On the other hand, within this framework, as compared to that of [8], we are no longer confined to linear dependence on the fields of Lagrange multipliers. Remarkably, the generating equation introducing the gauge admits of a solution which is identical with the gauge-fixing functional found in the original version of [5], and which, in particular, includes the well-known gauge-fixing condition of the BV formalism.…”

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.…”