Remarks on the Sp(2)-covariant Lagrangian quantization of gauge theories

Abstract

The existence of a solution of the exact generating equations (with ℏ≠0) for the Sp(2)-covariant Lagrangian quantization scheme is established. The characteristic arbitrariness of this solution is also studied. The equivalence between the Sp(2)-covariant quantization and the standard one is proven.

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

“…We have shown in this letter that the antifield formalism for the combined BRST-anti-BRST symmetry developed in [7,8,9,10] can be given a geometric interpretation in terms of multivectors on the supermanifold of the fields. This extends the work of [6] to the anti-BRST context.…”

“…Hence, there is complete equivalence with the standard formalism, because the path integral does not depend on the choice of the non minimal sector. For another equivalence proof, see [9].…”

“…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…”

On Possible Generalizations of Field-Antifield Formalism

“…An Sp(2)-covariant version of the BV formalism has been proposed recently by Batalin, Lavrov and Tyutin [15,16,17].…”

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

“…Ghost and antighost variables, BRST and anti-BRST charges and the pair of equations for the effective action form Sp(2) doublets. In [2]- [7], the formal proof of the existence of a solution to the Sp(2) master equation and description of the arbitrariness of solutions were given. In those papers, however, the locality of the effective action was assumed as a hypothesis.…”