The Geometry of Heisenberg Groups - Ernst Binz, Sonja Pods

The Geometry of Heisenberg Groups

With Applications in Signal Theory, Optics, Quantization, and Field Quantization

, (Autoren)

Buch | Hardcover
299 Seiten
2009
American Mathematical Society (Verlag)
978-0-8218-4495-3 (ISBN)
139,95 inkl. MwSt
The three-dimensional Heisenberg group, being the simplest non-commutative Lie group, appears prominently in various applications of mathematics. This title intends to present basic geometric and algebraic properties of the Heisenberg group and its relation to other important mathematical structures and to describe some of its applications.
The three-dimensional Heisenberg group, being the simplest non-commutative 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 well 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.

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 three-space 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 3-space The Schrodinger representation and the metaplectic representation The Heisenberg group-A basic geometric background of signal analysis and geometric optics Quantization of quadratic polynomials Field theoretic Weyl quantization of a vector field in 3-space Thermodynamics, geometry and the Heisenberg group by Serge Preston Bibliography Index.

Erscheint lt. Verlag 30.1.2009
Reihe/Serie Mathematical Surveys and Monographs
Zusatzinfo Illustrations
Verlagsort Providence
Sprache englisch
Gewicht 723 g
Themenwelt Mathematik / Informatik Mathematik Angewandte Mathematik
Mathematik / Informatik Mathematik Geometrie / Topologie
ISBN-10 0-8218-4495-4 / 0821844954
ISBN-13 978-0-8218-4495-3 / 9780821844953
Zustand Neuware
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