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)