Noncommutative Quantum Mechanics Viewed from Feynman Formalism

Details Noncommutative Quantum Mechanics Viewed from Feynman Formalism Noncommutative Quantum Mechanics Viewed from Feynman Formalism

2007-09-06

arxiv.org/abs/0709.0816v2

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, To appear in the Proceedings of the Lorentz Workshop "Beyond the Quantum", eds. Th.M. Nieuwenhuizen et al., World Sc

Scientific paper

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.

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