Schroeren's new paper "Decoherent histories of spin networks" made me aware of some work by two people at Cambridge DAMTP and London Imperial's Blackett Lab on the(adsbygoogle = window.adsbygoogle || []).push({}); Quantum Zeno(QZ) effect in the path integral e.g. decoherent histories (DH) context.

Schroeren's paper: http://arxiv.org/abs/1206.4553

Gell-Mann and Hartle's recent DH paper http://arxiv.org/abs/1106.0767

Halliwell and Yearsley's recent QZ paper: http://arxiv.org/abs/1205.3773

Pitfalls of Path Integrals: Amplitudes for Spacetime Regions and the Quantum Zeno Effect

J.J.Halliwell, J.M.Yearsley

(Submitted on 16 May 2012)

Path integrals appear to offer natural and intuitively appealing methods for defining quantum-mechanical amplitudes for questions involving spacetime regions. For example, the amplitude for entering a spatial region during a given time interval is typically defined by summing over all paths between given initial and final points but restricting them to pass through the region at any time. We argue that there is, however, under very general conditions, a significant complication in such constructions. This is the fact that the concrete implementation of the restrictions on paths over an interval of time corresponds, in an operator language, to sharp monitoring at every moment of time in the given time interval. Such processes suffer from the quantum Zeno effect --the continual monitoring of a quantum system in a Hilbert subspace prevents its state from leaving that subspace. As a consequence, path integral amplitudes defined in this seemingly obvious way have physically and intuitively unreasonable properties and in particular, no sensible classical limit. In this paper we describe this frequently-occurring but little-appreciated phenomenon in some detail, showing clearly the connection with the quantum Zeno effect. We then show that it may be avoided by implementing the restriction on paths in the path integral in a "softer" way. The resulting amplitudes then involve a new coarse graining parameter, which may be taken to be a timescale ε, describing the softening of the restrictions on the paths. We argue that the complications arising from the Zeno effect are then negligible as long as ε >> 1/ E, where E is the energy scale of the incoming state.

24 pages, 6 figures.

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# Solving the Quantum Zeno problem with path integral QG

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