Operators in Quantum Mechanics and Model System II

A. J. Leggett

R. Fukuda

Models are presented as examples in order to illustrate the previously proposed theory of measurement in quantum mechanics [R. Fukuda, Phys. Rev. A 35, 8 (1987)]. It is based on the specific structure of the Hilbert space of the macroscopic system. It is shown that after the interaction of an object with a detector we have to prepare the exponential of the extensive operators to recover the interference which is lost in the measuring process.

Philip Franklin

Mauricio Mondragón, Alejandro Pérez, Carlo Rovelli C

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.