Search results for "Geometric quantization"

Geometric quantization in the presence of an electromagnetic field

1983

Some aspects of the formalism of geometric quantization are described emphasizing the role played by the symmetry group of the quantum system which, for the free particle, turns out to be a central extensionG(m) of the Galilei groupG. The resulting formalism is then applied to the case of a particle interacting with the electromagnetic field, which appears as a necessary modification of the connection 1-form of the quantum bundle when its invariance group is generalized to alocal extension ofG. Finally, the quantization of the electric charge in the presence of a Dirac monopole is also briefly considered.

Relativistic wave equations from supergroup quantization

1983

A formalism of geometric quantization recently introduced which is based on the consideration of Lie groups which are central extensions by U(1) is applied to the relativistic case by using the N-2 super Poincare group with a central charge.

DEFORMATION QUANTIZATION OF COADJOINT ORBITS

2000

A method for the deformation quantization of coadjoint orbits of semisimple Lie groups is proposed. It is based on the algebraic structure of the orbit. Its relation to geometric quantization and differentiable deformations is explored.

Star Products on Coadjoint Orbits

2000

We study properties of a family of algebraic star products defined on coadjoint orbits of semisimple Lie groups. We connect this description with the point of view of differentiable deformations and geometric quantization.

Algebraic Quantization, Good Operators and Fractional Quantum Numbers

1995

The problems arising when quantizing systems with periodic boundary conditions are analysed, in an algebraic (group-) quantization scheme, and the ``failure" of the Ehrenfest theorem is clarified in terms of the already defined notion of {\it good} (and {\it bad}) operators. The analysis of ``constrained" Heisenberg-Weyl groups according to this quantization scheme reveals the possibility for new quantum (fractional) numbers extending those allowed for Chern classes in traditional Geometric Quantization. This study is illustrated with the examples of the free particle on the circumference and the charged particle in a homogeneous magnetic field on the torus, both examples featuring ``anomal…

QUANTIZATION OPERATORS ON QUADRICS

2008

Topological Hopf Algebras, Quantum Groups and Deformation Quantization

2019

After a presentation of the context and a brief reminder of deformation quantization, we indicate how the introduction of natural topological vector space topologi es on Hopf algebras associated with Poisson Lie groups, Lie bialgebras and their doubles explains their dualities a nd provides a comprehensive framework. Relations with deformation quantization and applications to the deformation quantization of symmetric spaces are described.