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

[摘要] The definition of the Hamiltonian operator H for a general wave equation 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 asan 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 "representation" (e.g. transforming the Dirac wave function from the "Dirac representation" to a "Foldy-Wouthuy senre presentation"). We also assert that the energy operator ought to be well defined in a given reference frame at a given time, e.g. by comparing the situation for this operator with the main features of the energy for a classical Hamiltonian particle.

[发布机构] Laboratory Soils, Solids, Structures, Risks, CNRS, Université Grenoble-Alpes, Grenoble, France^1

[效力级别] 力学 [学科分类] 力学，机械学

[关键词] Co-ordinate system;Curved spacetime;Dirac particles;Energy operators;Hamiltonian operators;Hermitians;Reference frame;Time dependent