General Triplectic Quantization

TL;DR

This paper extends the triplectic quantization framework by providing invariant operator expressions, a geometric interpretation of key operators, and a consistent approach to second class hyperconstraints in the field-antifield formalism.

Contribution

It introduces more invariant generating operators, offers a geometric explanation for the V^a operator, and generalizes the calculus of forms for the triplectic quantization.

Findings

Invariant expressions for generating operators derived.

Geometric interpretation of the V^a operator provided.

A consistent treatment of second class hyperconstraints established.

Abstract

The general structure of the Sp(2) covariant version of the field-antifield quantization of general constrained systems in the Lagrangian formalism, the so called triplectic quantization, as presented in our previous paper with A.M.Semikhatov is further generalized and clarified. We present new unified expressions for the generating operators which are more invariant and which yield a natural realization of the operator V^a and provide for a geometrical explanation for its presence. This V^a operator provides then for an invariant definition of a degenerate Poisson bracket on the triplectic manifold being nondegenerate on a naturally defined submanifold. We also define inverses to nondegenerate antitriplectic metrics and give a natural generalization of the conventional calculus of exterior differential forms which e g explains the properties of these inverses. Finally we define and give a consistent treatment of second class hyperconstraints.