Galilean Tensor Calculus

Galilean transformations are expressed as transformations in a five-dimensional space, with a subsidiary condition, and a Galilean tensor calculus with a nonsingular metric is developed. It is shown that the homogeneous Galilei group is isomorphic to a subgroup of the pseudo-orthogonal group O(4, 1), which leaves the difference of two components of a vector invariant. A set of scalar variables for a Galilean-invariant S matrix is selected. A Galilean-invariant phase space is defined and a recursion relation derived.