2005/11/30 by Michel Leclerc, M. Leclerc · 2 citations
Physics and Astronomy · #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Non-Hermitian Physics #gr-qc
paper · pdf · doi:10.1088/0264-9381/23/12/001
published as Class.Quant.Grav. 23 (2006) 4013 · 9 pages, final version, to appear in Class. Quant. Grav
arxiv created 2006/05/05 · openalex publication_date 2006/05/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
It is shown by a straightforward argument that the Hamiltonian generating the time evolution of the Dirac wavefunction in relativistic quantum mechanics is not Hermitian with respect to the covariantly defined inner product whenever the background metric is time dependent. An alternative, Hermitian, Hamiltonian is found and shown to be directly related to the canonical field Hamiltonian used in quantum field theory.