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

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