which is a Hamilton-Jacobi equation that can be solved with the method of characteristics, meaning that this partial differential equation (PDE) is replaced by an infinite set of ordinary differential equations (ODEs) for the characteristics, i.e., the trajectories, along which the PDE is always satisfied. The ODEs have the form given in Eqs. ( ) and (10), where, under a specific gauge choice, the force becomes F α ν (t) = Ȧα ν (t), which yields