The geometry of Heisenberg groups : with applications in signal theory, optics, quantization, and field quantization
著者
書誌事項
The geometry of Heisenberg groups : with applications in signal theory, optics, quantization, and field quantization
（Mathematical surveys and monographs, v. 151）
American Mathematical Society, c2008
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注記
"With an appendix by Serge Preston."
Includes bibliographical reference (p. 289-294) and index
内容説明・目次
内容説明
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.
目次
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.
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