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  3. Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology
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  • Publisher:
    Cambridge University Press
    Publication date:
    05 January 2012
    15 December 2011
    ISBN:
    9781139108782
    9781107610491
    DOI:
    https://doi.org/10.1017/CBO9781139108782
    Dimensions:
    Weight & Pages:
    Dimensions:
    (228 x 152 mm)
    Weight & Pages:
    0.43kg, 284 Pages
    • Subjects:
    Mathematics (general), Mathematics, Physics and Astronomy, Theoretical Physics and Mathematical Physics, Geometry and Topology
    Series:
    London Mathematical Society Lecture Note Series (397)
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    Subjects:
    Mathematics (general), Mathematics, Physics and Astronomy, Theoretical Physics and Mathematical Physics, Geometry and Topology
    Series:
    London Mathematical Society Lecture Note Series (397)
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    Book description

    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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