Mathematics of the Quantum Zeno Effect
arXiv:math-ph/0307044
Abstract
We present an overview of the mathematics underlying the quantum Zeno effect. Classical, functional analytic results are put into perspective and compared with more recent ones. This yields some new insights into mathematical preconditions entailing the Zeno paradox, in particular a simplified proof of Misra's and Sudarshan's theorem. We empahsise the complex-analytic structures associated to the issue of existence of the Zeno dynamics. On grounds of the assembled material, we reason about possible future mathematical developments pertaining to the Zeno paradox and its counterpart, the anti-Zeno paradox, both of which seem to be close to complete characterisations.
32 pages, 1 figure, AMSLaTeX. In: Mathematical Physics Research at the Leading Edge, Charles V. Benton ed. Nova Science Publishers, Hauppauge NY, pp. 111-141, ISBN 1-59033-905-3, 2003; revision contains corrections from the published corrigenda to Reference [64]
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