Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 009, 40 pages      arXiv:1401.6507      https://doi.org/10.3842/SIGMA.2014.009
Contribution to the Special Issue on Noncommutative Geometry and Quantum Groups in honor of Marc A. Rieffel

The Heisenberg Relation - Mathematical Formulations

Richard V. Kadison a and Zhe Liu b
a) Department of Mathematics, University of Pennsylvania, USA
b) Department of Mathematics, University of Central Florida, USA

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

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).

Key words: Heisenberg relation; unbounded operator; finite von Neumann algebra; Type II1 factor.

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