The Wigner problem in electrodynamics


Abstract: The relation between canonical commutation rules and a shape of acting force is analysed. It is shown that canonical commutation relations and Newtonian equations of motion for a single particle dynamics do imply the force to be of the Lorentz type but the inverse is not true. The example of a single particle motion in a constant magnetic field shows that equations of motion allow an alternative to canonical commutation relations to exist and it is a Lie algebra. The algebra found is of the type of algebras found in studies leading towards noncommutative geometry approaches to physical problems.


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