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Ch. 1 The Skew Field of Quaternions 1
Ch. 2 Elements of the Geometry of S[superscript 3], Hopf Bundles and Spin Representations 25
Ch. 3 Internal Variables of Singularity Free Vector Fields in a Euclidean Space 47
Ch. 4 Isomorphism Classes, Chern Classes and Homotopy Classes of Singularity Free Vector Fields in 3-Space 73
Ch. 5 Heisenberg Algebras, Heisenberg Groups, Minkowski Metrics, Jordan Algebras and SL(2,C) 107
Ch. 6 The Heisenberg Group and Natural C[superscript *]-Algebras of a Vector Field in 3-Space 131
Ch. 7 The Schrodinger Representation and the Metaplectic Representation 161
Ch. 8 The Heisenberg Group: A Basic Geometric Background of Signal Analysis and Geometric Optics 191
Ch. 9 Quantization of Quadratic Polynomials 215
Ch. 10 Field Theoretic Weyl Quantization of a Vector Field in 3-Space 247
Appendix A Thermodynamics, Geometry and the Heisenberg Group by Serge Preston 269
Bibliography 291
Index 295
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Ryan Batty
reviewed The Geometry of Heisenberg Groups: With Applications in Signal Theory, Optics, Quantization, and Field Quantization on January 29, 2018 The Geometry of Heisenberg Groups
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