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The Geometry of Heisenberg Groups: With Applications in Signal Theory, Optics, Quantization, and Field Quantization

Ernst Binz and Sonja Pods
Publisher: 
American Mathematical Society
Publication Date: 
2008
Number of Pages: 
299
Format: 
Hardcover
Series: 
Mathematical Surveys and Monographs 151
Price: 
85.00
ISBN: 
9780821844953
Category: 
Monograph
We do not plan to review this book.

1. The skew field of quaternions

2. Elements of the geometry of S3, 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 three-space

5. Heisenberg algebras, Heisenberg groups, Minkowski metrics, Jordan algebras and SL(2,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

Appendix: Thermodynamics, geometry and the Heisenberg group by Serge Preston

Bibliography

Index

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