On Dirac-like equations in 2n-dimensional spaces

The naturally IOsub(4,2) covariant spinor field equations GAMMAsub(a)(d/d etasub(a))xi(eta) = 0 and GAMMAsub(a)(d/d etasub(a))xi(eta) = GAMMA7phi(eta)xi(eta) in pseudo-Euclidean space Msup(4,2) of which the first may be derived from the definition of pure conformal semi-spinors and the second from the one of pure conformal spinors, are first reduced, with the Dirac method, to a five-dimensional projective space and then solved exactly with respect to the fifth variable, which is then eliminated with an invariant procedure, bringing them to a system of equations in Minkowski space-time Msup(3,1). The conformal (generalized) covariance of the original system is spontaneously broken, as a consequence of the exact (partial) solutions, and generates, in Msup(3,1), a system of spinor field equations for a doublet of interacting 'canonical' Dirac spinors presenting (the first) Poincare-Weyl x U1 and the second x SU2 internal symmetry, the latter having the same form as in the well-known Yukawa equation for the nucleon interacting with an external pseudoscalar pion field. In case of Weyl x internal covariance one of the two Dirac spinors of the conformal doublet presents a vectorlike interaction identical to that characterizing 'exotic' spinors on a non-simply-connected manifold (torus). The geometrical meaning of the Uacting in the spin space of the Dirac-spinor doublet contained in the conformal spinor. The same U1 also appears, in the obtained equations in Msup(3,1) as a local gauge transformation for only one of the two Dirac spinors of the doublet (the 'exotic' one), which, being the equations covariant with respect to these U1 transformations implies a conserved 'charge' for the corresponding fermion. The first equation presents solutions apt to reproduce the main features of weak interactions