Reflection symmetric Erdelyi-Kober type operators - a quasi-particle interpretation

TL;DR

This paper introduces reflection symmetric Erdélyi-Kober fractional integral operators to model fractional quasi-particle systems, providing analytical eigenfunctions and eigenvalues, and explores their implications for fractional quantum models of residual pairing interactions.

Contribution

It develops a novel fractional quantum model using reflection symmetric Erdélyi-Kober operators, including analytical solutions and a new interpretation of residual interactions.

Findings

Analytical eigenfunctions and eigenvalues for the operators

Definition of fractional creation and annihilation operators

Interpretation as a fractional quantum model for pairing interactions

Abstract

Reflection symmetric Erd$\acute{\text{e}}$lyi-Kober type fractional integral operators are used to construct fractional quasi-particle generators. The eigenfunctions and eigenvalues of these operators are given analytically. A set of fractional creation- and annihilation-operators is defined and the properties of the corresponding free Hamiltonian are investigated. Analogue to the classical approach for interacting multi-particle systems the results are interpreted as a fractional quantum model for a description of residual interactions of pairing type.