Geometric Analysis on the Heisenberg Group and Its Generalizations

Erscheinungsjahr 2007
ISBN: 978-0-8218-4319-2
Verlag: American Mathematical Society

Buch, Englisch, Band 40, 244 Seiten, Gewicht: 624 g

Reihe: AMS/IP Studies in Advanced Mathematics

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 Schrodinger's equation. One of the novelties of this book is the introduction of techniques from complex Hamiltonian mechanics. Information for our distributors: Titles in this series are co-published with International Press, Cambridge, MA.

Zielgruppe

Graduate students and research mathematicians interested in sub-Riemannian geometry and connections to quantum mechanics

Autoren/Hrsg.

Calin, Ovidiu

Chang, Der-Chen

Greiner, Peter

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie

Inhaltsverzeichnis

Geometric mechanics on the Heisenberg group

Geometric analysis of step 4 case

The geometric analysis of step $2(k+1)$ case

Geometry on higher dimensional Heisenberg groups

Complex Hamiltonian mechanics

Quantum mechanics on the Heisenberg group

Bibliography

Index

Über Autor(innen)

Ovidiu Calin, Eastern Michigan University, Ypsilanti, MI; Der-Chen Chang, Georgetown University, Washington, DC; Peter Greiner, University of Toronto, ON, Canada