Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces

• Main Author: Shchepetilov, Alexey V. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Series: Lecture Notes in Physics, 707
• Subjects: Physics.; Differential geometry.; Mechanics.; Mathematical Methods in Physics.; Differential Geometry.

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 space...

Table of Contents:

• Two-Point Homogeneous Riemannian Spaces
• Differential Operators on Smooth Manifolds
• Algebras of Invariant Differential Operators on Unit Sphere Bundles Over Two-Point Homogeneous Riemannian Spaces
• Hamiltonian Systems with Symmetry and Their Reduction
• Two-Body Hamiltonian on Two-Point Homogeneous Spaces
• Particle in a Central Field on Two-Point Homogeneous Spaces
• Classical Two-Body Problem on Two-Point Homogeneous Riemannian Spaces
• Quasi-Exactly Solvability of the Quantum Mechanical Two-Body Problem on Spheres.