Sheaves in Quantum Topos Induced by Quantization

Details Sheaves in Quantum Topos Induced by Quantization Sheaves in Quantum Topos Induced by Quantization

2011-08-25

arxiv.org/abs/1109.1192v2

Physics

Mathematical Physics

48pages

Scientific paper

This paper shows that quantization induces a Lawvere-Tierney topology on (hence, a sheaf topos in) the quantum topos. We show that a quantization map from classical observables to self-adjoint operators on a Hilbert space naturally induces geometric morphisms from presheaf topoi related to the classical system into a presheaf topos, called the quantum topos, on the context category consisting of commutative von Neumann algebras of bounded operators on the Hilbert space. By means of the geometric morphisms, we define Lawvere-Tierney topologies on the quantum topos (and their equivalent Grothendieck topologies on the context category). We show that, among them, we can uniquely select the most informative one, which we call the quantization topology. We furthermore construct sheaves induced by the quantization topology. This can be done in an elementary and self-contained way, because the quantization topology has a quite simple expression.

Affiliated with

Also associated with

No associations

Rating

Sheaves in Quantum Topos Induced by Quantization does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Sheaves in Quantum Topos Induced by Quantization, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sheaves in Quantum Topos Induced by Quantization will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-502975