A new concept of deformation quantization, I. Normal order quantization on cotangent bundles
Pflaum, Markus J.
arXiv, 9604144 / Harvested from arXiv
Text on arXiv
In this work we give a deformation theoretical approach to the problem of quantization. First the notion of a deformation of a noncommutative ringed space over a commutative locally ringed space is introduced within a language coming from Algebraic Geometry and Complex Analysis. Then we define what a Dirac quantization of a commutative ringed space with a Poisson structure, the space of classical observables, is. Afterwards the normal order quantization of the Poisson space of classical polynomial observables on a cotangent bundle is constructed. By using a complete symbol calculus on manifolds we succeed in extending the normal order quantization of polynomial observables to a quantization of a Poisson space of symbols on a cotangent bundle. Furthermore we consider functorial properties of these quantizations. Altogether it is shown that a deformation theoretical approach to quantization is possible not only in a formal sense but also such that the deformation parameter $\hbar$ can attain any real value.
Publié le : 1996-04-23
Classification:  High Energy Physics - Theory,  Mathematical Physics 
@article{9604144,
     author = {Pflaum, Markus J.},
     title = {A new concept of deformation quantization, I. Normal order quantization
  on cotangent bundles},
     journal = {arXiv},
     volume = {1996},
     number = {0},
     year = {1996},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9604144}
}

Pflaum, Markus J. A new concept of deformation quantization, I. Normal order quantization
  on cotangent bundles. arXiv, Tome 1996 (1996) no. 0, . http://gdmltest.u-ga.fr/item/9604144/