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

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.