Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology

Jens Bolte

ISBN 10: 1107610494 / ISBN 13: 9781107610491

Published by Cambridge University Press, 2012

About this Item

Druck auf Anfrage Neuware - Printed after ordering - Hyperbolic geometry is a classical subject in pure mathematics which has exciting applications in theoretical physics. In this book leading experts introduce hyperbolic geometry and Maass waveforms and discuss applications in quantum chaos and cosmology. The book begins with an introductory chapter detailing the geometry of hyperbolic surfaces and includes numerous worked examples and exercises to give the reader a solid foundation for the rest of the book. In later chapters the classical version of Selberg's trace formula is derived in detail and transfer operators are developed as tools in the spectral theory of Laplace-Beltrami operators on modular surfaces. The computation of Maass waveforms and associated eigenvalues of the hyperbolic Laplacian on hyperbolic manifolds are also presented in a comprehensive way. This book will be valuable to graduate students and young researchers, as well as for those experienced scientists who want a detailed exposition of the subject.

Seller Inventory # 9781107610491

Bibliographic Details

• Title: Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology
• Publisher: Cambridge University Press
• Publication Date: 2012
• Language: English
• ISBN 10: 1107610494
• ISBN 13: 9781107610491
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 229W x 152H x 17D millimeters 229 millimeters width by 152 millimeters height by 17 millimeters depth
• Weight: 468 grams

About this title

Synopsis

Hyperbolic geometry is a classical subject in pure mathematics which has exciting applications in theoretical physics. In this book leading experts introduce hyperbolic geometry and Maass waveforms and discuss applications in quantum chaos and cosmology. The book begins with an introductory chapter detailing the geometry of hyperbolic surfaces and includes numerous worked examples and exercises to give the reader a solid foundation for the rest of the book. In later chapters the classical version of Selberg's trace formula is derived in detail and transfer operators are developed as tools in the spectral theory of Laplace–Beltrami operators on modular surfaces. The computation of Maass waveforms and associated eigenvalues of the hyperbolic Laplacian on hyperbolic manifolds are also presented in a comprehensive way. This book will be valuable to graduate students and young researchers, as well as for those experienced scientists who want a detailed exposition of the subject.

About the Authors

Jens Bolte joined the Department of Mathematics at Royal Holloway, University of London, in 2007. He works in the field of quantum chaos and is, in particular, interested in arithmetic quantum chaos, semiclassical quantum mechanics and quantum graph models.

Frank Steiner is a Professor at Ulm University. He has spent sabbaticals at CERN and the Universities of Geneva, Lausanne, Paris and Princeton. His present areas of research are quantum graph models and cosmology.