Mathematical Surveys and Monographs 2008; 299 pp; hardcover Volume: 151 ISBN10: 0821844954 ISBN13: 9780821844953 List Price: US$88 Member Price: US$70.40 Order Code: SURV/151
 The threedimensional Heisenberg group, being a quite simple noncommutative Lie group, appears prominently in various applications of mathematics. The goal of this book is to present basic geometric and algebraic properties of the Heisenberg group and its relation to other important mathematical structures (the skew field of quaternions, symplectic structures, and representations) and to describe some of its applications. In particular, the authors address such subjects as signal analysis and processing, geometric optics, and quantization. In each case, the authors present necessary details of the applied topic being considered. With no prerequisites beyond the standard mathematical curriculum, this book manages to encompass a large variety of topics being easily accessible in its fundamentals. It can be useful to students and researchers working in mathematics and in applied mathematics. Readership Graduate students and research mathematicians interested in the use of analysis on Heisenberg groups to various problems in pure and applied mathematics. Table of Contents  The skew field of quaternions
 Elements of the geometry of \(S^3\), 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 threespace
 Heisenberg algebras, Heisenberg groups, Minkowski metrics, Jordan algebras and SL\((2,\mathbb{C})\)
 The Heisenberg group and natural \(C*\)algebras of a vector field in 3space
 The Schrödinger representation and the metaplectic representation
 The Heisenberg groupA basic geometric background of signal analysis and geometric optics
 Quantization of quadratic polynomials
 Field theoretic Weyl quantization of a vector field in 3space
 Thermodynamics, geometry and the Heisenberg group by Serge Preston
 Bibliography
 Index
