Based on the Caputo definition of the fractional derivative the ground state spectra of mesons are classified as multiplets of the fractional rotation group. The comparison with the experimental values leads to the conclusion, that quarks carry an up to now unrevealed fractional multiplicative quantum number, which we call fractional hyper charge.

The definition of the standard differential operator is extended from integer steps to arbitrary stepsize. The classical, nonrelativistic Hamiltonian is quantized, using these new continuous… Expand

Based on the Riemann fractional derivative the Casimir operators and multiplets for the fractional extension of the rotation group SO(n) are calculated algebraically. The spectrum of the… Expand

The definition of the standard differential operator is extended from integer steps to arbitrary stepsize. The classical, nonrelativistic Hamiltonian is quantized, using these new continuous… Expand

We study the charmonium, upsilon and strangeonium systems with a linear+Coulomb potential, in the high αs regime. Our approach is based on the Bethe-Salpeter equation, in ladder approximation, and… Expand

The spectrum of charmonium in the presence of a charmed-meson continuum is investigated. Radiative rates are in considerably better agreement with data than for the naive model, the largest… Expand