Toward exact solutions of the nonlinear Heisenberg–Pauli–Weyl spinor equation

In color geometrodynamics fundamental spinor fields are assumed to obey a GL(2f,C)⊗GL(2c,C) gauge‐invariant nonlinear spinor equation of the Heisenberg–Pauli–Weyl type. Quark confinement, assimilating a scheme of Salam and Strathdee, is (partially) mediated by the tensor ’’gluons’’ of strong gravity. This hypothesis is incorporated into the model by considering the nonlinear Dirac equation in a curved space‐time of hadronic dimensions. Disregarding internal degrees of freedom, it is then feasible, for a peculiar background space‐time, to obtain exact solutions of the spherical bound‐state problem. Finally, these solutions are tentatively interpreted as droplet‐type solitons and remarks on their interrelation with Wheeler’s geon construction are made.