  The dynamics of a particle moving in background electromagnetic and
gravitational fields is revisited from a Lie group cohomological perspective.
Physical constants characterising the particle appear as central extension
parameters of a group which is obtained from a centrally extended kinematical
group (Poincare or Galilei) by making local some subgroup. The corresponding
dynamics is generated by a vector field inside the kernel of a presymplectic
form which is derived from the canonical left-invariant one-form on the
extended group. A non-relativistic limit is derived from the geodesic motion
via an Inonu-Wigner contraction. A deeper analysis of the cohomological
structure reveals the possibility of a new force associated with a non-trivial
mixing of gravity and electromagnetism leading to in principle testable
predictions.
