Current Algebraic Structures over Manifolds: Poisson Algebras, q-Deformations and Quantization
High Energy Physics - Theory
2009-10-30 v1 alg-geom
Algebraic Geometry
Quantum Algebra
q-alg
Abstract
Poisson algebraic structures on current manifolds (of maps from a finite dimensional Riemannian manifold into a 2-dimensional manifold) are investigated in terms of symplectic geometry. It is shown that there is a one to one correspondence between such current manifolds and Poisson current algebras with three generators. A geometric meaning is given to q-deformations of current algebras. The geometric quantization of current algebras and quantum current algebraic maps is also studied.
Cite
@article{arxiv.hep-th/9603114,
title = {Current Algebraic Structures over Manifolds: Poisson Algebras, q-Deformations and Quantization},
author = {Sergio Albeverio and Shao-Ming Fei},
journal= {arXiv preprint arXiv:hep-th/9603114},
year = {2009}
}
Comments
25 pages, Latex