  Dyson published in 1990 a proof due to Feynman of the Maxwell equations. This
proof is based on the assumption of simple commutation relations between
position and velocity. We first study a nonrelativistic particle using Feynman
formalism. We show that Poincar\'{e}'s magnetic angular momentum and Dirac
magnetic monopole are the direct consequences of the structure of the sO(3) Lie
algebra in Feynman formalism. Then we show how to extend this formalism to the
dual momentum space with the aim of introducing Noncommutative Quantum
Mechanics which was recently the subject of a wide range of works from particle
physics to condensed matter physics.
