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

7th International Workshop DICE2014 Spacetime – Matter – Quantum Mechanics

物理学;力学

Arminjon, Mayeul^1

Laboratory Soils, Solids, Structures, Risks, CNRS, Université Grenoble-Alpes, Grenoble, France^1

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

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/626/1/012030/pdf
DOI  :  10.1088/1742-6596/626/1/012030

学科分类：力学，机械学

来源: IOP

【 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.