The covariance problem and the Hamiltonian formalism in quantum mechanics
Abstract
The traditional approach to the covariance problem in quantum mechanics is inverted and the spacetime transformations are assumed as the basic unknowns, according to the prescription that the correspondence principle and the commutation rules must be covariant. It is shown that the only solutions are either Galilean or Lorentzian (including the possibility of an imaginary lightvelocity c^{2}< 0). The Dirac formalism for the waveequation and the condition c^{2}> 0 are obtained simoultaneously as the unique solution, provided that the Hamiltonian is Hermitean (in the usual sense), and the internal degrees of freedom allow for a finitedimensional representation. Infinitedimensional representations are introduced in order to extend the Hamiltonian formalism to other spinors.
 Publication:

Foundations of Physics
 Pub Date:
 May 1989
 DOI:
 10.1007/BF00734661
 Bibcode:
 1989FoPh...19..579F