Determination of the Electromagnetic Lagrangian from a System of Poisson Brackets

Author: Bracken, Paul

Source: International Journal of Theoretical Physics, Volume 44, Number 1, January 2005 , pp. 127-138(12)

Publisher: Springer

Buy & download fulltext article:

Price: $47.00 plus tax (Refund Policy)

Abstract:

The Lagrangian and Hamiltonian formulations of electromagnetism are reviewed and the Maxwell equations are obtained from the Hamiltonian for a system of many electric charges. It is shown that three of the equations which were obtained from the Hamiltonian, namely the Lorentz force law and two Maxwell equations, can be obtained as well from a set of postulated Poisson brackets. It is shown how the results derived from these brackets can be used to reconstruct the original Lagrangian for the theory aided by some reasoning based on physical concepts.

Keywords: Poisson bracket; Maxwell equations; Lagrangian

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10773-005-1489-z

Affiliations: 1: Department of Mathematics, University of Texas, Edinburgh, Texas, 78541-2999, Email: bracken@panam.edu

Publication date: 2005-01-01