Abstract
The dynamics of a particle moving in background electromagnetic and gravitational fields is revisited from a Lie group cohomological perspective. Physical constants characterizing the particle appear as central extension parameters of a group which is obtained from a centrally extended kinematical group (Poincaré or Galilei) by making some subgroup local. The corresponding dynamics is generated by a vector field inside the kernel of a pre-symplectic form which is derived from the canonical left-invariant 1-form on the extended group. A non-relativistic limit is derived from the geodesic motion via an Inönü–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.