2009/03/30 by Christoph Nölle, Nölle, Christoph
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.0903.5336
openalex publication_date 2009/03/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations we find a compatibility condition restricting the set of admissible connections. In the special case when phase space is a cotangent bundle this compatibility condition has many solutions, and the resulting quantum theory not only reproduces the well-known geometric quantization scheme, but also allows to quantize all interesting observables. For Kähler manifolds there is no compatibility condition, but a canonical choice for the parameters. The explicit form of the observables however remains undetermined.