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Geometric Analysis on the Heisenberg Group and Its Generalizations
Ovidiu Calin, Eastern Michigan University, Ypsilanti, MI, Der-Chen Chang, Georgetown University, Washington, DC, and Peter Greiner, University of Toronto, ON, Canada
A co-publication of the AMS and International Press.
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2007; 244 pp; hardcover
Volume: 40
ISBN-10: 0-8218-4319-2
ISBN-13: 978-0-8218-4319-2
List Price: US$61 Member Price: US$48.80
Order Code: AMSIP/40

The theory of subRiemannian manifolds is closely related to Hamiltonian mechanics. In this book, the authors examine the properties and applications of subRiemannian manifolds that automatically satisfy the Heisenberg principle, which may be useful in quantum mechanics. In particular, the behavior of geodesics in this setting plays an important role in finding heat kernels and propagators for Schrödinger's equation. One of the novelties of this book is the introduction of techniques from complex Hamiltonian mechanics.

Titles in this series are co-published with International Press, Cambridge, MA.

Graduate students and research mathematicians interested in subRiemannian geometry and connections to quantum mechanics.

Reviews

"...a resource for pure and applied mathematicians and theoretical physics working in quantum mechanics. One of the authors' most interesting innovations is introducing the complex Hamiltonian mechanics techniques and use them to describe the fundamental solutions and heat propagators in quantum mechanics. ...result is fresh and livelywhile also being thorough. The authors provide exercises for each chapter."

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