Abstract
In this chapter we study the algebra DiffI (QS) of invariant differential operators on the unit sphere bundle QS over a two-point homogeneous Riemannian space Q. Namely we construct a system of generators and relations for these algebras. These generators will appear in Chap. 5 in explicitly invariant expressions of two-body Hamiltonian operators H on the space Q. On the other hand, the center of the algebra DiffI (QS) commutes with H, i.e., it consists of integrals for the quantum two-body problem on Q
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© 2006 Springer
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Shchepetilov, A.V. (2006). Algebras of Invariant Differential Operators on Unit Sphere Bundles Over Two-Point Homogeneous Riemannian Spaces. In: Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces. Lecture Notes in Physics, vol 707. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-35386-0_3
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DOI: https://doi.org/10.1007/3-540-35386-0_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35384-3
Online ISBN: 978-3-540-35386-7
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