Abstract
We explore the relation between (spectral) noncommutative geometry and quantum mechanics. We consider a dynamical model based on a triple , which mimics aspects of the spectral formulation of general relativity. Its phase space is the space of on-shell Dirac operators. We construct the corresponding quantum theory using a covariant canonical quantization. The Connes distance between two states over (“spacetime points”) turns out discrete and we compute its spectrum. The quantum states of the geometry form a Hilbert space , and is promoted to an operator on . The triple can be viewed as the quantization of the triples .
- Received 9 April 1999
DOI:https://doi.org/10.1103/PhysRevLett.83.1079
©1999 American Physical Society