  Fermions on a cylinder coupled to gravity and gauge fields are examined by
studying the geometric action associated with the symmetries of such a system.
The gauge coupling constant is shown to be constrained and the effect of
gravity on the masses is discussed. Furthermore, we introduce a new
gravitational theory which couples to the fermions by promoting the coadjoint
vector of the diffeomorphism sector to a dynamical variable. This system,
together with the gauge sector is shown to be equivalent to a one dimensional
system.
