Bessel Process and Conformal Quantum Mechanics

TL;DR

This paper explores the deep mathematical relationship between Bessel processes and conformal quantum mechanics, including their generalizations and underlying symmetries, to enhance understanding of their interconnected structures.

Contribution

It investigates the connection between Bessel processes and conformal quantum mechanics, including generalizations and the role of conformal symmetry.

Findings

Analysis of self-adjoint extensions of CQM

Discussion of Bessel process generalizations

Insights into conformal group structures

Abstract

Different aspects of the connection between the Bessel process and the conformal quantum mechanics (CQM) are discussed. The meaning of the possible generalizations of both models is investigated with respect to the other model, including self adjoint extension of the CQM. Some other generalizations such as the Bessel process in the wide sense and radial Ornstein- Uhlenbeck process are discussed with respect to the underlying conformal group structure.