Hermitian vector fields and covariant quantum mechanics of a spin particle

Details Hermitian vector fields and covariant quantum mechanics of a spin particle Hermitian vector fields and covariant quantum mechanics of a spin particle

2009-09-09

arxiv.org/abs/0909.1797v1

Int.J.Geom.Meth.Mod.Phys.7:599-623,2010

Physics

Mathematical Physics

23 pages

Scientific paper

10.1142/S0219887810004464

In the context of Covariant Quantum Mechanics for a spin particle, we classify the ``quantum vector fields'', i.e. the projectable Hermitian vector fields of a complex bundle of complex dimension 2 over spacetime. Indeed, we prove that the Lie algebra of quantum vector fields is naturally isomorphic to a certain Lie algebra of functions of the classical phase space, called ``special phase functions''. This result provides a covariant procedure to achieve the quantum operators generated by the quantum vector fields and the corresponding observables described by the special phase functions.

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