2018/11/19 by Edwin J Beggs, Beggs, Edwin J
Mathematics · Physics and Astronomy · #46L30 #58B34 #83C65 #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #hep-th #math.OA #math.QA #msc:46L30 #msc:58B34 #msc:83C65
paper · pdf · doi:10.48550/arxiv.1811.07601
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
arxiv created 2019/08/20 · arxiv updated 2019/08/21
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 M2(C) and C(Zn), 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.