2010/01/31 by M. CHAICHIAN, M. Chaichian, M. OKSANEN +5
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1142/s0217751x10049785
published as Int.J.Mod.Phys.A25:3765-3796,2010 · AMS-LaTeX, 27 pages. v2: minor corrections in presentation and language, added one reference
arxiv created 2010/07/05 · openalex publication_date 2010/07/30 · arxiv updated 2010/09/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
A covariant Poisson bracket and an associated covariant star product in the sense of deformation quantization are defined on the algebra of tensor-valued differential forms on a symplectic manifold, as a generalization of similar structures that were recently defined on the algebra of (scalar-valued) differential forms. A covariant star product of arbitrary smooth tensor fields is obtained as a special case. Finally, we study covariant star products on a more general Poisson manifold with a linear connection, first for smooth functions and then for smooth tensor fields of any type. Some observations on possible applications of the covariant star products to gravity and gauge theory are made.