On extending the quantum measure

Dowker, Fay; Johnston, Steven; Surya, Sumati

Please use this identifier to cite or link to this item: http://hdl.handle.net/2289/3996

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DC Field	Value	Language
dc.contributor.author	Dowker, Fay	-
dc.contributor.author	Johnston, Steven	-
dc.contributor.author	Surya, Sumati	-
dc.date.accessioned	2011-04-08T06:50:59Z	-
dc.date.available	2011-04-08T06:50:59Z	-
dc.date.issued	2010-12-17	-
dc.identifier.citation	Journal of Physics A, 2010, Vol. 43, p505305	en
dc.identifier.issn	1751-8113	-
dc.identifier.issn	1751-8121-(Online)	-
dc.identifier.uri	http://hdl.handle.net/2289/3996	-
dc.description	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)	en
dc.description.abstract	We point out that a quantum system with a strongly positive quantum measure or decoherence functional gives rise to a vector-valued measure whose domain is the algebra of events or physical questions. This gives an immediate handle on the question of the extension of the decoherence functional to the sigma algebra generated by this algebra of events. It is on the latter that the physical transition amplitudes directly give the decoherence functional. Since the full sigma algebra contains physically interesting questions, like the return question, extending the decoherence functional to these more general questions is important. We show that the decoherence functional, and hence the quantum measure, extends if and only if the associated vector measure does. We give two examples of quantum systems whose decoherence functionals do not extend: one is a unitary system with finitely many states, and the other is a quantum sequential growth model for causal sets. These examples fail to extend in the formal mathematical sense and we speculate on whether the conditions for extension are unphysically strong.	en
dc.language.iso	en	en
dc.publisher	IOP Publishing Ltd.	en
dc.relation.uri	http://arxiv.org/abs/1007.2725	en
dc.relation.uri	http://iopscience.iop.org/1751-8121/43/50/505305/	en
dc.relation.uri	http://adsabs.harvard.edu/abs/2010JPhA...43X5305D	en
dc.rights	2010 IOP Publishing Ltd.	en
dc.title	On extending the quantum measure	en
dc.type	Article	en
Appears in Collections:	Research Papers (TP)

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