  This article expands for spinor fields the recently developed Dynamical
Bridge formalism which relates a linear dynamics in a curved space to a
nonlinear dynamics in Minkowski space. Astonishingly, this leads to a new
geometrical mechanism to generate a chiral symmetry breaking without mass,
providing an alternative explanation for the undetected right-handed neutrinos.
We consider a spinor field obeying the Dirac equation in an effective curved
space constructed by its own currents. This way, both chiralities of the spinor
field satisfy the same dynamics in the curved space. Subsequently, the
dynamical equation is re-expressed in terms of the flat Minkowski space and
then each chiral component behaves differently. The left-handed part of the
spinor field satisfies the Dirac equation while the right-handed part is
trapped by a Nambu-Jona-Lasinio (NJL) type potential.
