Abstract
The traditional approach to the covariance problem in quantum mechanics is inverted and the space-time transformations are assumed as the basicunknowns, according to the prescription that the correspondence principle and the commutation rules must becovariant. It is shown that the only solutions are either Galilean or Lorentzian (including the possibility of an imaginary light-velocity c2<0). The Dirac formalism for the wave-equation and the condition c2>0 are obtained simoultaneously as theunique solution, provided that the Hamiltonian is Hermitean (in the usual sense), and the internal degrees of freedom allow for afinite-dimensional representation. Infinite-dimensional representations are introduced in order to extend the Hamiltonian formalism to other spinors.
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This work was partially supported by Ministero della Pubblica Istruzione.
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Ferrari, L. The covariance problem and the Hamiltonian formalism in quantum mechanics. Found Phys 19, 579–605 (1989). https://doi.org/10.1007/BF00734661
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DOI: https://doi.org/10.1007/BF00734661