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The Decoherent Histories Approach to Quantum Mechanics

J. J. Halliwell

Astrophysics and space science libraryJan 1, 19970 citations

Quantum mechanics and decoherent histories

J. Weyers

AIP conference proceedingsJan 1, 19940 citations

Symmetries of decoherence functionals

S. Schreckenberg

The basic ingredients of the “consistent histories” approach to quantum theory are a space 𝒰𝒫 of “history propositions” and a space 𝒟 of “decoherence functionals.” In this article we consider such history quantum theories in the case where 𝒰𝒫 is given by the set of projectors 𝒫(𝒱) on some Hilbert space 𝒱. Using an analog of Wigner’s theorem in the context of history quantum theories proven earlier, we develop the notion of a “symmetry of a decoherence functional” and prove that all such symmetries form a group which we call “the symmetry group of a decoherence functional.” We calculate for the case of standard quantum mechanics—when looked at from the perspective of the history program—some of these symmetries explicitly and relate them to some discussions that have appeared previously.The basic ingredients of the “consistent histories” approach to quantum theory are a space 𝒰𝒫 of “history propositions” and a space 𝒟 of “decoherence functionals.” In this article we consider such history quantum theories in the case where 𝒰𝒫 is given by the set of projectors 𝒫(𝒱) on some Hilbert space 𝒱. Using an analog of Wigner’s theorem in the context of history quantum theories proven earlier, we develop the notion of a “symmetry of a decoherence functional” and prove that all such symmetries form a group which we call “the symmetry group of a decoherence functional.” We calculate for the case of standard quantum mechanics—when looked at from the perspective of the history program—some of these symmetries explicitly and relate them to some discussions that have appeared previously.

arXiv:gr-qc/9607050Journal of Mathematical PhysicsFeb 1, 199715 citations

Decoherence in quantum mechanics

Jurjen F. Koksma, Tomislav Prokopec, Michael G. Schmidt

arXiv:1012.3701Annals of PhysicsJan 5, 201115 citations

Hilbert spaces from path integrals

Fay Dowker, Steven Johnston, Rafael D Sorkin

It is shown that a Hilbert space can be constructed for a quantum system starting from a framework in which histories are fundamental. The Decoherence Functional provides the inner product on this "History Hilbert space". It is also shown that the History Hilbert space is the standard Hilbert space in the case of non-relativistic quantum mechanics.

arXiv:1002.0589Journal of Physics A Mathematical and TheoreticalJun 9, 201023 citations

0 Hilbert Spaces from Path Integrals

Fay Dowker B, Steven Johnston, Rafael D. Sorkin

It is shown that a Hilbert space can be constructed for a quantum system starting from a framework in which histories are fundamental. The Decoherence Functional provides the inner product on this “History Hilbert space”. It is also shown that the History Hilbert space is the standard Hilbert space in the case of non-relativistic quantum mechanics. 1

Jan 1, 201043 citations

Homogeneous Decoherence Functionals¶in Standard and History Quantum Mechanics

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Homogeneous Decoherence Functionals¶in Standard and History Quantum Mechanics

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