Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces (Lecture Notes in Physics (707))

Shchepetilov, Alexey V.

ISBN 10: 3642071279 / ISBN 13: 9783642071270

Published by Springer, 2010

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Bibliographic Details

• Title: Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces (Lecture Notes in Physics (707))
• Publisher: Springer
• Publication Date: 2010
• Language: English
• ISBN 10: 3642071279
• ISBN 13: 9783642071270
• Binding: Paperback
• Condition: Like New
• Book Type: book

About this title

Synopsis

Mathematics develops both due to demands of other sciences and due to its internal logic. The latter fact explains the attention of mathematicians to many problems, which are in close connection with basic mathematical notions, even if these problems have no direct practical applications. It is well known that the space of constant curvature is one of the basic geometry notion [208], which induced the wide ?eld for investigations. As a result there were found numerous connections of constant curvature spaces with other branches of mathematics, for example, with integrable partial dif- 1 ferential equations [36, 153, 189] and with integrable Hamiltonian systems [141]. Geodesic ?ows on compact surfaces of a constant negative curvature (with the genus 2) generate many test examples for ergodic theory (see also 3 [183] and the bibliography therein). The hyperbolic space H (R) is the space of velocities in special relativity (see Sect. 7.4.1) and also arises as space-like sections in some models of general relativity.

From the Back Cover

The present monograph gives a short and concise introduction to classical and quantum mechanics on two-point homogenous Riemannian spaces, with empahsis on spaces with constant curvature. Chapter 1-4 provide the basic notations from differential geometry for studying two-body dynamics in these spaces. Chapter 5 deals with the problem of finding explicitly invariant expressions for the two-body quantum Hamiltonian. Chapter 6 addresses one-body problems in a central potential. Chapter 7 studies the classical counterpart of the quantum system of chapter 5. Chapter 8 investigates some applications in the quantum realm, namely for the coulomb and oscillator potentials.