From Gauging Nonrelativistic Translations to N-Body Dynamics

We consider the gauging of space translations with time–dependent gauge functions. Using fixed time gauge of relativistic theory, we consider the gauge– invariant model describing the motion of nonrelativistic particles. When we use gauge–invariant nonrelativistic velocities as independent variables the translation gauge fields enter the equations through a d × (d + 1) matrix of vielbein fields and their Abelian field strengths, which can be identified with the torsion tensors of teleparallel formulation of relativity theory. We consider the planar case (d = 2) in some detail, with the assumption that the action for the dreibein fields is given by the translational Chern–Simons term. We fix the asymptotic transformations in such a way that the space part of the metric becomes asymptotically Euclidean. The residual symmetries are (local in e-mail: [email protected] email: [email protected] e-mail: [email protected]