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The Geometry of Heisenberg Groups: With Applications in Signal Theory, Optics, Quantization, and Field Quantization
About this Title
Ernst Binz, University of Mannheim, Mannheim, Germany and Sonja Pods, University of Mannheim, Mannheim, Germany. with an appendix by Serge Preston
Publication: Mathematical Surveys and Monographs
Publication Year:
2008; Volume 151
ISBNs: 978-0-8218-4495-3 (print); 978-1-4704-1378-1 (online)
DOI: https://doi.org/10.1090/surv/151
MathSciNet review: MR2435327
MSC: Primary 22E25; Secondary 22D25, 43A40, 43A65, 81S05, 94A12
ReadershipTable of Contents
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Front/Back Matter
Chapters
- 1. The skew field of quaternions
- 2. Elements of the geometry of $S^3$, Hopf bundles and spin representations
- 3. Internal variables of singularity free vector fields in a Euclidean space
- 4. Isomorphism classes, Chern classes and homotopy classes of singularity free vector fields in 3-space
- 5. Heisenberg algebras, Heisenberg groups, Minkowski metrics, Jordan algebras and SL$(2,\mathbb {C})$
- 6. The Heisenberg group and natural $C*$-algebras of a vector field in 3-space
- 7. The Schrödinger representation and the metaplectic representation
- 8. The Heisenberg group: A basic geometric background of signal analysis and geometric optics
- 9. Quantization of quadratic polynomials
- 10. Field theoretic Weyl quantization of a vector field in 3-space
- 11. Thermodynamics, geometry and the Heisenberg group by Serge Preston