Richard V. Kadison, Zhe Liu, “The Heisenberg Relation — Mathematical Formulations”, SIGMA, 2014, Volume 10,009, 40 pp.

This article is cited in 9 papers

The Heisenberg Relation — Mathematical Formulations

Richard V. Kadison^a, Zhe Liu^b

^a Department of Mathematics, University of Pennsylvania, USA
^b Department of Mathematics, University of Central Florida, USA

Abstract: We study some of the possibilities for formulating the Heisenberg relation of quantum mechanics in mathematical terms. In particular, we examine the framework discussed by Murray and von Neumann, the family (algebra) of operators affiliated with a finite factor (of infinite linear dimension).

Keywords: Heisenberg relation; unbounded operator; finite von Neumann algebra; Type II$_1$ factor.

MSC: 47L60; 47L90; 46L57; 81S99

Received: July 26, 2013; in final form January 18, 2014; Published online January 25, 2014

Language: English

DOI: 10.3842/SIGMA.2014.009