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International Journal of Theoretical Physics

, Volume 44, Issue 1, pp 127–138 | Cite as

Determination of the Electromagnetic Lagrangian from a System of Poisson Brackets

  • Paul Bracken
Article

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.

KEY WORDS

Poisson bracket Maxwell equations Lagrangian 

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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TexasEdinburgh

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