From Feynman proof of Maxwell equations to noncommutative quantum mechanics

@inproceedings{Berard2007FromFP,
  title={From Feynman proof of Maxwell equations to noncommutative quantum mechanics},
  author={Alain B'erard and Herv'e Mohrbach and Jos{\'e} Lages and Pierre R{\'e}al Gosselin and Yves Grandati and H. Boumrar and Ferhat Menas},
  year={2007}
}
In 1990, Dyson published a proof due to Feynman of the Maxwell equations assuming only the commutation relations between position and velocity. With this minimal assumption, Feynman never supposed the existence of Hamiltonian or Lagrangian formalism. In the present communication, we review the study of a relativistic particle using "Feynman brackets." We show that Poincare's magnetic angular momentum and Dirac magnetic monopole are the consequences of the structure of the Lorentz Lie algebra… 

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