The geometric quantization procedure follows the principle of canonical quantization by replacing a Poisson bracket of smooth functions on a Poisson manifold with a commutator product of operators in ...

Algebraic quantum theory usually deals with Hilbert spaces. This Chapter addresses quantum models involving Hilbert manifolds and Hilbert bundles, but we restrict our consideration to particular ...

Gauge theories underpin our understanding of fundamental interactions by enforcing invariance under continuous symmetry transformations. Quantization of such theories requires careful treatment of ...

The Proposal explores new structures on classical geometric objects, like manifolds, vector bundles, etc., that can be interpreted, most naturally, from the point of view of noncommutative, rather ...