Triplectic quantization: A geometrically covariant description of the Sp(2)-symmetric Lagrangian formalism

• Published in: Nuclear physics. B 1995-07, Vol.446 (1), p.249-285
• Main Authors: Batalin, I.A., Marnelius, R., Semikhatov, A.M.
• Format: Article
• Language: English
• ISSN: 0550-3213; 1873-1562
• DOI: 10.1016/0550-3213(95)00176-S

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.