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.
HORZELA, ANDRZEJ (1999) "The Wigner problem in electrodynamics," Turkish Journal of Physics: Vol. 23: No. 5, Article 11. Available at: https://journals.tubitak.gov.tr/physics/vol23/iss5/11