The geometry of Heisenberg groups : [electronic resource] with applications in signal theory, optics, quantization, and field quantization / Ernst Binz, Sonja Pods ; with an appendix by Serge Preston.

9781470413781 (online)

Providence, R.I. : American Mathematical Society, c2008.

1 online resource (xvi, 299 p.)

Access is available to the Yale community.

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Print version: Binz, Ernst, 1939- geometry of Heisenberg groups :

Books / Online

English

February 11, 2020

Includes bibliographical references (p. 289-294) and index.

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