General triplectic quantization

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 non-degenerate on a naturally defined submanifold. We also define inverses to non-degenerate 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.