Galilean relativity and its invariant bilinear forms

Abstract

We construct the family of bilinear forms gG on R3+1 for which Galilean boosts and spatial rotations are isometries. The key feature of these bilinear forms is that they are parametrized by a Galilean invariant vector whose physical interpretation is rather unclear. At the end of the paper, we construct the Poisson bracket associated with the (nondegenerate) antisymmetric part of gG.

6 pages, typos corrected and text clarity improved