Relativistic equations of motion from Poisson brackets
The author reviews how the Maxwell pair arises from the basic set of fundamental Poisson brackets which may be postulated. In order to obtain the correct dynamics at the nonrelativistic level, one simply requires the basic Poisson brackets and an equation which determines the dynamics. It is duplicated by writing down an elementary Hamiltonian to generate the equations of motion. It is shown that this procedure can be generalized to the relativistic case in a rigorous way, in such a manner that there is manifest invariance under Lorentz transformations. The phase space with its coordinate functions is taken to define a differentiable manifold, and a Riemannian manifold is obtained by introducing the usual Minkowski metric. All dynamical variables are taken to be classical -- no quantization takes place.
scientific article; zbMATH DE number 1337997