Geometric Analysis on the Heisenberg Group and Its Generalizations (AMS/IP Studies in Advanced Mathematics) by Ovidiu Calin (PDF)

Description

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.

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⭐This is a nicely written book. The authors have been careful in including motivations for most of the topics discussed.

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