Dirac equation from the Hamiltonian and the case with a gravitational field

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dc.creatorArminjon, Mayeul
dc.date2005-12-07
dc.date2006-01-11
dc.date.accessioned2026-07-07T10:44:04Z
dc.date.available2026-07-07T10:44:04Z
dc.descriptionStarting from an interpretation of the classical-quantum correspondence, we derive the Dirac equation by factorizing the algebraic relation satisfied by the classical Hamiltonian, before applying the correspondence. This derivation applies in the same form to a free particle, to one in an electromagnetic field, and to one subjected to geodesic motion in a static metric, and leads to the same, usual form of the Dirac equation--in special coordinates. To use the equation in the static-gravitational case, we need to rewrite it in more general coordinates. This can be done only if the usual, spinor transformation of the wave function is replaced by the 4-vector transformation. We show that the latter also makes the flat-space-time Dirac equation Lorentz-covariant, although the Dirac matrices are not invariant. Because the equation itself is left unchanged in the flat case, the 4-vector transformation does not alter the main physical consequences of that equation in that case. However, the equation derived in the static-gravitational case is not equivalent to the standard (Fock-Weyl) gravitational extension of the Dirac equation.
dc.description27 pages, standard LaTeX. v2: minor style changes, accepted for publication in Found. Phys. Letters
dc.identifierhttps://arxiv.org/abs/gr-qc/0512046
dc.identifierhttp://arxiv.org/abs/gr-qc/0512046
dc.identifierFound.Phys.Lett.19:225-247,2006
dc.identifierdoi:10.1007/s10702-006-0514-7
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/182463
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectQuantum Physics
dc.titleDirac equation from the Hamiltonian and the case with a gravitational field
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