An Sp(2)-covariant quantization of gauge theories with linearly dependent generators

Abstract

The Sp(2)-symmetric version of covariant quantization is formulated for the general case of any stage-reducible gauge theories.

Geometric interpretation of the quantum master equation in the BRST—anti-BRST formalism

“…The choice ofK in (43) yields a path integral that is both BRST and anti-BRST invariant [7,8]. However, one may take a gauge fixingK that has a different structure without changing the integral.…”

“…Now, the integral (15) considered inJ [7,8] is precisely of the form (40). Indeed, one can write (16) as…”

“…Recently, Batalin, Lavrov and Tyutin have extended the antibracketantifield formalism in order to include the anti-BRST symmetry [7,8,9,10]. To that end, they associate with each field not just one antifield, but rather three antifields Φ * Aa (a = 1, 2) and Φ A of parity…”

“…In this extended formalism, the path integral having both BRST-invariance and anti-BRST invariance is given by [7,8] …”

Space-time locality in theSp(2)-symmetric Lagrangian formalism

“…To solve equation (6), it is helpful to introduce operators γ a , which contain derivatives ∂/∂L i , ∂/∂(R i α ϕ * ia ). To make the introducing of such operators possible we make the standard assumptions on the structure of the action S and of the gauge generators R i α , which we will call the regularity assumptions of the theory.…”