General quantum-mechanical setting for field-antifield formalism as a hyper-gauge theory

Abstract

A general quantum-mechanical setting is proposed for the field-antifield formalism as a unique hyper-gauge theory in the field-antifield space. We formulate a Schrödinger-type equation to describe the quantum evolution in a "current time" purely formal in its nature. The corresponding Hamiltonian is defined in the form of a supercommutator of the delta-operator with a hyper-gauge Fermion. The initial wave function is restricted to be annihilated with the delta-operator. The Schrödinger's equation is resolved in a closed form of the path integral, whose action contains the symmetric Weyl's symbol of the Hamiltonian. We take the path integral explicitly in the case of being a hyper-gauge Fermion an arbitrary function rather than an operator.

15 pages, new Section added, published version

References in corpus (6)

• Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism
• A systematic study of finite BRST-BV transformations in field-antifield formalism
• Odd Scalar Curvature in Anti-Poisson Geometry
• Odd Scalar Curvature in Field-Antifield Formalism
• Closed description of arbitrariness in resolving quantum master equation
• A systematic study of finite BRST-BV transformations within W-X formulation of the standard and the Sp(2)-extended field-antifield formalism

Cited by in corpus (1)

• Superfield generating equation of field-antifield formalism as a hyper-gauge theory