Connection between type B (or C) and F factorizations and construction of algebras

TL;DR

This paper explores how different factorization types of Hamiltonians relate to algebra construction, showing that satellite algebras are characteristic of type E factorizable Hamiltonians, with applications to the Coulomb problem.

Contribution

It extends previous work by demonstrating that Hamiltonians with type F factorizations can also lead to algebra constructions from types B or C, completing the classification.

Findings

Satellite algebras are characteristic of type E factorizable Hamiltonians.

Type F factorizations can generate algebras from types B or C.

The Coulomb problem exemplifies these algebraic connections.

Abstract

In a recent paper (Del Sol Mesa A and Quesne C 2000 J. Phys. A: Math. Gen. 33 4059), we started a systematic study of the connections among different factorization types, suggested by Infeld and Hull, and of their consequences for the construction of algebras. We devised a general procedure for constructing satellite algebras for all the Hamiltonians admitting a type E factorization by using the relationship between type A and E factorizations. Here we complete our analysis by showing that for Hamiltonians admitting a type F factorization, a similar method, starting from either type B or type C ones, leads to other types of algebras. We therefore conclude that the existence of satellite algebras is a characteristic property of type E factorizable Hamiltonians. Our results are illustrated with the detailed discussion of the Coulomb problem.