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Algebras of Invariant Differential Operators on Unit Sphere Bundles Over Two-Point Homogeneous Riemannian Spaces

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Part of the Lecture Notes in Physics book series (LNP,volume 707)

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

Keywords

  • Commutator Relation
  • Isometry Group
  • Riemannian Space
  • Independent Element
  • Algebra DiffI

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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