Two body problem on two point homogeneous spaces, invariant differential operators and the mass center concept

TL;DR

This paper investigates the two-body problem on two point homogeneous spaces using invariant differential operators, deriving Hamiltonian representations and exploring mass center definitions in these geometric contexts.

Contribution

It introduces a novel approach to express the two-body Hamiltonian on homogeneous spaces via invariant operators, linking mass center concepts to this framework.

Findings

Derived Hamiltonian representation using invariant differential operators.

Connected mass center definitions to Hamiltonian expressions.

Provided a new geometric perspective on the two-body problem.

Abstract

We consider the two body problem with central interaction on two point homogeneous spaces from point of view of the invariant differential operators theory. The representation of the two particle Hamiltonian in terms of the radial differential operator and invariant operators on the symmetry group is found. The connection of different mass center definitions for these spaces to the obtained expression for Hamiltonian operator is studied.