New insights in particle dynamics from group cohomology
arXiv:hep-th/0105278 · doi:10.1088/0305-4470/35/45/101
Abstract
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.
arXiv comment8 pages, LaTeX, no figures. To appear in J. Phys. A (Letter to the editor)