Relativistic equations of motion from Poisson brackets
type: Item
instance of: scholarly article
title: Relativistic equations of motion from Poisson brackets
zbMATH Open document ID: 0949.37036
DOI: 10.1023/A:1026680205982
author: Paul Bracken
published in: International Journal of Theoretical Physics
publication date: 2000-12-10T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 37J05
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 78A25
Mathematics Subject Classification ID: 70H40
zbMATH DE Number: 1337997
zbMATH Keywords: Poisson brackets
zbMATH Keywords: Maxwell equation
zbMATH Keywords: relativistic Hamiltonian
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1337997