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arXiv · hep-th/9502031

Triplectic Quantization: A Geometrically Covariant Description of the Sp(2)-symmetric Lagrangian Formalism

I Batalin·R Marnelius·A Semikhatov
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Abstract

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.

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I Batalin, R Marnelius, A Semikhatov. 1995-02-27. Triplectic Quantization: A Geometrically Covariant Description of the Sp(2)-symmetric Lagrangian Formalism. https://doi.org/10.1016/0550-3213(95)00176-s

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