A Heisenberg Algebra Bundle of a Vector Field in Three-Space and its Weyl Quantization

Journal Article · Wed Jan 04 00:00:00 EST 2006 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.2158712· OSTI ID:20787713

Binz, Ernst; Pods, Sonja ^[1]

---

1. Lehrstuhl fuer Mathematik I, Universitaet Mannheim, 68131 Mannheim (Germany)

In these notes we associate a natural Heisenberg group bundle Ha with a singularity free smooth vector field X = (id,a) on a submanifold M in a Euclidean three-space. This bundle yields naturally an infinite dimensional Heisenberg group H{sub X}{sup {infinity}}. A representation of the C*-group algebra of H{sub X}{sup {infinity}} is a quantization. It causes a natural Weyl-deformation quantization of X. The influence of the topological structure of M on this quantization is encoded in the Chern class of a canonical complex line bundle inside Ha.

• OSTI ID: 20787713
• Journal Information: AIP Conference Proceedings, Vol. 810, Issue 1; Conference: Vaxjo conference on quantum theory: Reconsideration of foundations - 3, Vaxjo (Sweden), 6-11 Jun 2005; Other Information: DOI: 10.1063/1.2158712; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
DEFORMATION
EUCLIDEAN SPACE
LIE GROUPS
QUANTIZATION
QUANTUM FIELD THEORY
SINGULARITY
TOPOLOGY
VECTOR FIELDS