Noncommutative geodesics and the KSGNS construction
Quantum Algebra
2019-08-21 v2 High Energy Physics - Theory
Operator Algebras
Abstract
We study geodesics in noncommutative geometry by means of bimodule connections and completely positive maps using the Kasparov, Stinespring, Gel'fand, Naimark & Segal (KSGNS) construction. This is motivated from classical geometry, and we also consider examples on the algebras M_2(C) and C(Z_n), though restricting to classical real time. On the way we have to consider the reality of a noncommutative vector field, and for this we propose a definition depending on a state on the algebra.
Cite
@article{arxiv.1811.07601,
title = {Noncommutative geodesics and the KSGNS construction},
author = {Edwin J Beggs},
journal= {arXiv preprint arXiv:1811.07601},
year = {2019}
}
Comments
Version 2: Major revision - the main change is the inclusion of a reality condition on vector fields which enforces normalisation of states. The examples have been recomputed to include this