TRIPLECTIC QUANTIZATION - A GEOMETRICALLY COVARIANT DESCRIPTION OF THE SP(2)-SYMMETRICAL LAGRANGIAN-FORMALISM

A geometric description is given for the Sp(2) covariant version of the field-antifield quantization of general constrained systems in the Lagrangian formalism. We develop differential geometry on manifolds in which a basic set of coordinates (''fields'') have two superpartners (''antifields''). The quantization on such a triplectic manifold requires introducing several specific differential-geometric objects, whose properties we study, These objects are then used to impose a set of generalized master equations that ensure gauge-independence of the path integral. The theory thus quantized is shown to extend to a level-1 theory formulated on a manifold that includes antifields to the Lagrange multipliers. We also observe intriguing relations between triplectic and ordinary symplectic geometry.