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Lagrangian for the So-Called Non-Potential Systems: The Case of Magnetic Monopoles

In: Deformations of Mathematical Structures

Author

Listed:
  • Guy Laville

    (Université Pierre et Marie Curie, Mathématics, L.A. 213 du C.N.R.S.)

Abstract

We study two distinct cases. Firstly, we construct a lagrangian associated with the Newton equations mẍk= fk(x), 1≤k≤3, where fk are components of a force which depends only on the position (without the classical hypothesis of integrability for the force). For clarifying the idea, here we take the frame-work of the Newtonian mechanics. Secondly, we consider the quantum electrodynamics in the case where the field is generated by the magnetic and electric charges. Mathematically speaking, we perceive that we have to give up exterior differential calculus which is totally unsuitable here. We propose to treat these questions with “interior” differential calculus.

Suggested Citation

  • Guy Laville, 1989. "Lagrangian for the So-Called Non-Potential Systems: The Case of Magnetic Monopoles," Springer Books, in: Julian Ławrynowicz (ed.), Deformations of Mathematical Structures, pages 331-337, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-2643-1_30
    DOI: 10.1007/978-94-009-2643-1_30
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