Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-06-19
J.Phys.Conf.Ser.70:012004,2007
Physics
High Energy Physics
High Energy Physics - Theory
Presented at the 3rd Feynman Festival (Collage Park, Maryland, U.S.A., August 2006)
Scientific paper
10.1088/1742-6596/70/1/012004
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 Poincar\'e's magnetic angular momentum and Dirac magnetic monopole are the consequences of the structure of the Lorentz Lie algebra defined by the Feynman's brackets. Then, we extend these ideas to the dual momentum space by considering noncommutative quantum mechanics. In this context, we show that the noncommutativity of the coordinates is responsible for a new effect called the spin Hall effect. We also show its relation with the Berry phase notion. As a practical application, we found an unusual spin-orbit contribution of a nonrelativistic particle that could be experimentally tested. Another practical application is the Berry phase effect on the propagation of light in inhomogeneous media.
Boumrar Hocine
B{é}rard Alain
Gosselin Pierre
Grandati y.
Lages Jose
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