Construction of a faithful vector representation of the Newtonian description of space-time and the Galilei group (Q1895839)

A Newtonian set \(\{e_\mu\}\) is constructed from the full Clifford algebra \(C_{1,3}\) of space-time generated by the basis \(\{\gamma_\alpha\}\). The orthogonal set \(\{e_\mu\}\) has a group of transformations isomorphic to the homogeneous Galilei group. The transformations of this group are obtained explicitly in a vectorial formalism. The correspondence between the Lorentz and the Galilei transformations is given as well as a discussion of the properties of the Galilean coordinate system \((\tau, q^1, q^2, q^3)\). The parameter \(\tau\) is used as universal time and \(q = q^i e_i\) is the position in a three-dimensional vector space with Euclidean geometry. Some examples of particular Newtonian bases are analyzed in detail.