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 a hyper-gauge fermion being an arbitrary function rather than an operator.