On Fermi-like quantisation of classical mechanics
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In this work we generalise some previously obtained results concerning the quantisation of classical finite models according to the symmetric (Fermi-like) scheme of quantisation. We consider models whose dynamics is defined through some non-singular Lie bracket and show that we can make the dynamics with any prescribed bracket relations, as defined by a certain type ofnon-singular symmetric brackets, coexist. The quantisation scheme established is: (a) defined up to an arbitrary factor and, (b) sensitive to the addition of total time derivatives to the corresponding Lagrangian. Both unconstrained and constrained models are considered.
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