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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.
pdf (546 kb)
tex (49 kb)
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