An idea for quantization by means of geometric observables is explained, which is a kind of the sheaf theoretical methods. First the formulation of differential geometry by using the structure sheaf is explained. The point of view to get interesting noncommutative observable algebras of geometric fields is introduced. The idea is to deform the algebra by suitable interaction structures. As an example of such structures the Poisson-structure is mentioned and this leads naturally to deformation quantization.
@article{701613,
title = {Differential geometry over the structure sheaf: a way to quantum physics},
booktitle = {Proceedings of the 17th Winter School "Geometry and Physics"},
series = {GDML\_Books},
publisher = {Circolo Matematico di Palermo},
address = {Palermo},
year = {1998},
pages = {[45]-51},
mrnumber = {MR1662724},
zbl = {0945.58008},
url = {http://dml.mathdoc.fr/item/701613}
}
Fischer, Gerald. Differential geometry over the structure sheaf: a way to quantum physics, dans Proceedings of the 17th Winter School "Geometry and Physics", GDML_Books, (1998), pp. [45]-51. http://gdmltest.u-ga.fr/item/701613/