The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this… (More)

ing frames O (X ) coming from a topological space to general frames is a genuine generalization of the concept of a space, as plenty of frames exist tha t are not of the form O (X ). A simple example… (More)

We prove the existence of a strict deformation quantization for the canonical Poisson structure on the dual of an integrable Lie algebroid. It follows that any Lie groupoid C *-algebra may be… (More)

An adaptationof Rieffel’s notion of “strict deformation quantization” is applied to a particle moving on an arbitrary Riemannianmanifold Q in an externalgaugefield, that is, a connection on a… (More)

It is well known that rings are the objects of a bicategory, whose arrows are bimodules, composed through the bimodule tensor product. We give an analogous bicategorical description of C-algebras,… (More)

Symplectic reduction, also known as Marsden-Weinstein reduction, is an important construction in Poisson geometry. Following N.P. Landsman [22], we propose a quantization of this procedure by means… (More)

A strict quantization of a compact symplectic manifold S on a subset I ⊆ R, containing 0 as an accumulation point, is defined as a continuous field of C *-algebras {A } ∈I , with A0 = C0(S), and a… (More)

Beginning with Anderson (1972), spontaneous symmetry breaking (ssb) in infinite quantum systems is often put forward as an example of (asymptotic) emergence in physics, since in theory no finite… (More)

A new approach to the quantization of constrained or otherwise reduced classical mechanical systems is proposed. On the classical side, the generalized symplectic reduction procedure of Mikami and… (More)

Notwithstanding known obstructions to this idea, we formulate an attempt to turn quantization into a functorial procedure. We define a category Poisson of Poisson manifolds, whose objects are… (More)