The geometry of Heisenberg groups : with applications in signal theory, optics, quantization, and...

作者：  Ernst Binz, Sonja Pods ; with an appendix by Serge Preston.

出版社：

简介：Written for graduate students of both fields, this volume examines and connects the mathematics and physics of Heisenberg groups. Ten chapters discuss the skew field of quaternions; elements of the geometry of S3, Hopf bundles, and spin representations; internal variables of singularity free vector fields in a Euclidean space; isomorphism classes, Chern classes, and homotopy classes of singularity free vector fields in 3-space; Heisenberg algebras, Heisenberg groups, Minkowski metrics, Jordan algebras, and special linear groups; the Heisenbreg group and natural C*-algebras of a vector field in 3-space; the Schr枚dinger representation and the metaplectic representation; the Heisenberg group as a basic geometric background of signal analysis and geometric optics; quantization of quadratic polynomials; and field theoretic Weyl quantization of a vector field in 3-space. Also included is an appendix on thermodynamics, geometry, and the Heisenberg group. Minimal prerequisites include background in linear algebra and elementary differential geometry. Annotation 漏2009 Book News, Inc., Portland, OR (booknews.com)