Homogeneous rank one perturbations and inverse square potentials

TL;DR

This paper explores exactly solvable families of operators, including singular rank one perturbations and inverse square potential Schrödinger operators, highlighting their interconnectedness and renormalization group flows.

Contribution

It establishes a close relationship between rank one perturbations and inverse square potential Schrödinger operators, expanding understanding of their solvable structures.

Findings

Identification of solvable operator families

Connection between perturbations and inverse square potentials

Observation of renormalization group flows

Abstract

Following [D,BDG,DR], I describe several exactly solvable families of closed operators. Some of these families are defined by the theory of singular rank one perturbations. The remaining families are Schrodinger operators with inverse square potentials and various boundary conditions. I describe a close relationship between these families. In all of them one can observe interesting renormalization group flows (action of the group of dilations).