Chapter 19: The Galilei Group

The Galilei group is the first of the two groups of space-time transformations to be discussed in this book. For brevity we refer to it as G. This group expresses the geometrical invariance properties of the equations of motion of a non-relativistic classical dynamical system when the system is isolated from external influences. This is so to the extent that these equations of motion are reasonable generalizations of the Newtonian equations of motion for multi particle systems experiencing interparticle forces. If the dynamics of the system can be conveyed via an action principle, so that a Lagrangian and therefore a Hamiltonian description is possible, then the system is described by a classical canonical realization of G…