Neutron to proton mass difference, parton distribution functions and baryon resonances from dynamics on the Lie group u(3)

We develop a hamiltonian framework on the Lie group u(3), which we call allospace and which is supposed to carry all the colour dynamics needed to describe the baryon spectrum. The energy eigenstates of our particular Schrödinger equation tends to predict realistically all certain baryon resonances in the N-Deltasector. The grouping and number of resonances is predicted by the model from a single fitting of the ground state N(939). The Hamiltonian also contains terms from the group space Laplacian to take care of spin and the superimposed hypercharge and isospin flavour structure. Scarce neutral flavour singlet resonances are predicted and may show up around 4500 MeV in neutron diffraction dissociation experiments above the threshold in the free charm system SigmaCplus(2455)Dminus. They should also be visible in photoproduction of pPiMinus on neutrons and lower lying singlets may show up in pPiMinus invariant mass in B decays. We give a controversial prediction of the relative neutron to proton mass difference 0.138 % as originating in period doublings of certain parametric states. The group space dynamics communicates with real space via the exterior derivative which projects out quark and gluon fields from the allospatial state. The allostate in turn is excited from space by the momentum operators which act as toroidal generators on the group manifold. Such generators can be used to trace out parton distribution functions and examples are shown to mimic the valence quark content of the proton.