2007/04/30 by Mauricio Mondragon, Mauricio Mondragón, Alejandro Perez +2 · 1 citation
Physics and Astronomy · #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #gr-qc
paper · pdf · doi:10.1103/physrevd.76.064005
published as Phys.Rev.D76:064005,2007
arxiv created 2007/04/30 · openalex publication_date 2007/09/10 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We introduce a simple quantum mechanical model in which time and space are discrete and periodic. These features avoid the complications related to continuous-spectrum operators and infinite-norm states. The model provides a tool for discussing the probabilistic interpretation of generally covariant quantum systems, without the confusion generated by spurious infinities. We use the model to illustrate the formalism of general-relativistic quantum mechanics, and to test the definition of multiple-event probability introduced in a companion paper [Phys. Rev. D 75, 084033 (2007)]. We consider a version of the model with unitary time evolution and a version without unitary time evolution.