1995/02/27 by I Batalin, I.A. Batalin, R. Marnelius +3
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Covariant transformation #Differential geometry #Formalism (music) #Homotopy and Cohomology in Algebraic Topology #Lagrangian #Lagrangian system #Manifold (fluid mechanics) #Noncommutative and Quantum Gravity Theories #Quantization (signal processing) #Symplectic geometry #Symplectic manifold #hep-th
paper · pdf · doi:10.1016/0550-3213(95)00176-s
published as Nucl.Phys. B446 (1995) 249-285 · Revised version -- our treatment in Section 5 has been extended and several pedagogical notes inserted in Sections 2--4; more references added.
arxiv created 1995/02/27 · openalex publication_date 1995/07/01 · arxiv updated 2013/07/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.