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arXiv · 1502.04085

On the Hamiltonian and energy operators in a curved spacetime, especially for a Dirac particle

Mayeul Arminjon
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Abstract

The definition of the Hamiltonian operator H for a general wave equa-tion in a general spacetime is discussed. We recall that H depends on the coordinate system merely through the corresponding reference frame. When the wave equation involves a gauge choice and the gauge change is time-dependent, H as an operator depends on the gauge choice. This dependence extends to the energy operator E, which is the Hermitian part of H. We distinguish between this ambiguity issue of E and the one that occurs due to a mere change of the "represen-tation" (e.g. transforming the Dirac wave function from the "Dirac representation" to a "Foldy-Wouthuysen representation"). We also assert that the energy operator ought to be well defined in a given ref-erence frame at a given time, e.g. by comparing the situation for this operator with the main features of the energy for a classical Hamilto-nian particle.

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Mayeul Arminjon. 2015-02-13. On the Hamiltonian and energy operators in a curved spacetime, especially for a Dirac particle. https://doi.org/10.1088/1742-6596/626/1/012030

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