The Geometry of Heisenberg Groups: With Applications in Signal Theory, Optics, Quantization, and Field Quantization

Ernst Binz

ISBN 10: 0821844954 / ISBN 13: 9780821844953

Published by American Mathematical Society, 2008

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Bibliographic Details

• Title: The Geometry of Heisenberg Groups: With Applications in Signal Theory, Optics, Quantization, and Field Quantization
• Publisher: American Mathematical Society
• Publication Date: 2008
• Language: English
• ISBN 10: 0821844954
• ISBN 13: 9780821844953
• Binding: Hardback
• Condition: New
• Weight: 756 grams

About this title

Synopsis

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 Schrödinger 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 ©2009 Book News, Inc., Portland, OR (booknews.com)