| In an earlier paper we showed development of a bilocal baryon-meson field from two quark-antiquark fields. In the local approximation the hadron field was shown to exhibit supersymmetry which was then extended to hadronic mother trajectories and to inclusion of multiquark states. The Hamiltonian in the case of vanishing quark masses was shown to have a very good agreement with experiments. The theory for vanishing mass was solved using confluent hypergeometric functions. In order to solve the spin-free Hamiltonian with light quark masses we are led to develop a totally new kind of special function theory in mathematics that generalize all existing theories of confluent hypergeometric types. We call it the ‘Grand Confluent Hypergeometric Function.’ Our new solution produces previously unknown extra “hidden” quantum numbers relevant for description of supersymmetry and for generating new mass formulas.;Furthermore, we show for the first time how to solve mathematical equations having three term recursion relations and go on producing the exact solutions of some of the well-known special function theories that include Mathieu, Heun, Lame and the Grand Confluent Hypergeometric Function. We hope these new functions and their solutions will produce remarkable new range of applications not only in supersymmetric field theories as is shown here, but in the areas of all different classes of mathematical physics, applied mathematics and in engineering applications. |
