Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology
eBook - PDF

Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology

About this book

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.

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Yes, you can access Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology by Jens Bolte,Frank Steiner in PDF and/or ePUB format, as well as other popular books in Mathematics & Topology. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Cambridge University Press
Year
2011
Print ISBN
9781107610491
eBook ISBN
9781139382632
Topic
Mathematics
Subtopic
Topology
Index
Mathematics

Table of contents

  1. Cover
  2. Series Page
  3. Title
  4. Copyright
  5. Contents
  6. List of Contributors
  7. Preface
  8. I. Hyperbolic Geometry
  9. II. Selberg’s Trace Formula: An Introduction
  10. III. Semiclassical Approach to Spectral Correlation Functions
  11. IV. Transfer Operators, the Selberg Zeta Function and the Lewis-Zagier Theory of Period Functions
  12. V. On the Calculation of Maass Cusp Forms
  13. VI. Maass Waveforms on (Γ0(N), χ) (Computational Aspects)
  14. VII. Numerical Computation of Maass Waveforms and an Application to Cosmology
  15. Index