Histories Formulations of Quantum Theory  

Consistent Histories
* Idea: A closed quantum system is a Hilbert space, and every statement about it a subspace of H (no hidden variables); A history is a sequence of subspaces E1, E2, ..., associated with times t1, t2, ...; If a history is in a consistent family, it can be assigned a probability; Within that family, one and only one history occurs (notion of trajectory); The unitary time evolution generated by the Schrödinger equation is used to define consistent histories and calculate probabilities; Measurements play no fundamental role, they influence the history but one can talk of the behavior of quantum systems in the absence of measurement; In details, consistent historians differ.
* Motivation: Formulate quantum mechanics in a more covariant way; Find an interpretation that is less instrumentalist than the Copenhagen one, and more realist.

References > s.a. formulations of quantum mechanics; path-integral formulation.
@ General: Gell-Mann & Hartle in(90)-a1803; Hartle ViA(93)gq/92; Gell-Mann & Hartle PRD(93)gq/92, gq/94; Griffiths PRL(93); Dowker & Kent PRL(95)gq/94; Omnès 94; Diósi PLA(95)gq/94; Schreckenberg JMP(96)gq; Finkelstein qp/96 [interpretational questions]; McElwaine PhD(96)qp/97 [approximate consistency]; Caticha qp/98 [assumptions]; Kent PRL(98)gq; Wright CMP(99) [symmetries]; Savvidou PhD(99)gq [continuous time]; Brun qp/03-proc [resolving ambiguities]; Henson JPCS(09)-a0901 [and correspondence principle]; Sorkin a1004-in; Hohenberg a1101-wd [and interpretation]; Riedel et al PRA(16)-a1312 [and quantum Darwinism, redundant records]; Friedberg & Hohenberg RPP(14)-a1405 [Compatible Quantum Theory]; Hartle a1608 [starting with records of what histories happen].
@ Reviews: Halliwell gq/93-in, qp/03-proc; Dowker & Kent JSP(96)gq/94; Kent PS(98)gq; Griffiths & Omnès PT(99)aug; Griffiths 01; Dass qp/05-ln; Chisholm JPCS(09)qp/06; Hohenberg RMP(10)-a0909 [intro]; Griffiths a1105 [and consistent quantum ontology]; Hartle a1901 [cosmology and quantum theory]; Rodrigues Rocha et al a2103-in [history].
@ Choice of consistent set: McElwaine PRA(96)qp/95, PRA(97)qp/96; Kent & McElwaine PRA(97)gq/96; Griffiths PRA(98)qp/97; Anastopoulos IJTP(98)qp/97; Losada & Laura AP(14) [generalized contexts].
@ Decoherence functionals: Isham & Linden JMP(94)gq; Isham et al JMP(94)gq; Wright CMP(98); Dowker & Wilkes a2011 [strong positivity].
@ Continuous: Isham & Linden JMP(95)gq; Isham et al JMP(98)qp/97; Anastopoulos JMP(01)qp/00; Kouletsis PhD(00)gq/01.
@ Topos theory: Isham IJTP(97)gq/96; Raptis qp/01; Flori JMP(10).
@ Other generalized: Isham JMP(94)gq/93, qp/95-conf; Pulmannová IJTP(95); Goldstein & Page PRL(95); Rudolph IJTP(96)qp/95, JMP(98); Kent a1305 [real path quantum theory]; Halliwell PRA(17)-a1704 [incompatible consistent sets of histories].
@ Probabilities: Nisticò CMP(00); Saunders Syn(98)qp/01, qp/01-in; Anastopoulos IJTP(03) [quantum vs stochastic]; Hartle PRA(04)qp [virtual]; Marlow AP(06)qp/05, IJTP(06) [Bayesian account], qp/06 [and Gleason's theorem]; Jordan & Chisholm PLA(09)-a0801 [and weak decoherence]; Sudbery a2012.
@ Problems: Peruzzi & Rimini FPL(98)qp/97 [retrodictions]; Bassi & Ghirardi JSP(00)qp/99 [and realism], reply Griffiths JSP(00)qp; Nisticò PE(03)qp; Okon & Sudarsky FP(14)-a1301, a1504 [interpretational problems, measurement].
@ In quantum cosmology: Hartle in(93)gq/92, in(93)gq, in(95)gq/93, in(94)gq [and closed systems]; Kessari CQG(07)gq/06; Halliwell IJTP(06); Craig & Singh FP(11)-a1001, AIP(10); Kent a1204-proc [conditioning on the occurrence of a fixed sequence of cosmological events]; Craig & Singh CQG(13)-a1306 [in lqc + scalar], a1603-MG14 [probability of a non-singular bounce]; Craig IJMPD-a1604 [rev]; Lloyd a1608 [and the cosmological measure problem].
@ Other systems and topics: Griffiths qp/95, PRA(96)qp [quantum reasoning]; Kent LNP(00)gq/96 [subspace implications].
> Specific types of systems: see parametrized systems; QED; quantum field theory in curved spacetime; quantum constrained systems.

Related Topics > s.a. causality; entanglement and spacetime [entangled-history states]; locality in quantum theory; logic [anhomomorphic logic].
@ And contrary inferences: Kent PRL(97)gq/96, comment Griffiths & Hartle PRL(98)gq/97; Kent PRL(98)gq.
@ And Bohmian mechanics: Kent in(96)qp/95; Griffiths PLA(99)qp; Hiley & Maroney qp/00; Hartle PRA(04)qp/02.
@ And no-hidden-variables: Bassi & Ghirardi PLA(99)gq/98 [problem]; Griffiths PLA(00)qp/99 [no problem].
@ And measurement: d'Espagnat PLA(87); Brun PRA(00)qp/97 [continuous]; Sokolovski & Liu PLA(01); Lloyd qp/05 [generalized]; Seidewitz FP(11) [measurements in spacetime]; Griffiths PRA(13)-a1308 [restrictions on what an observer can know about a quantum system]; Okon & Sudarsky SHPMP-a1309; Griffiths a1501 [comparison with alternative approaches]; Ghazi-Tabatabai a1610 [observer dependence]; > s.a. zeno effect.
@ And decoherence: Paz & Zurek PRD(93)gq [environment-induced]; Halliwell PRD(01)qp/00 [approximate].
@ Geometry and structures: Craig qp/97 [geometry]; Dass & Joglekar AP(01) [symmetries]; Blute et al gq/01 [on graphs].
@ Phase space representation: Anastopoulos JMP(01)qp/00, AP(03)qp/02 [in phase space]; Larsson ht/04 [histories phase space, harmonic oscillator and free scalar]; Burch JMP(07)qp [perturbation theory, oscillator].
@ Other approaches: Raptis et al IJTP(07) [tomographic histories representation]; Leffler a1302 [different approach]; Cotler & Wilczek PS(16)-a1502 [quantum history states]; Castellani a1810 [history operator]; Diaz et al PRD(19)-a1910 [history state formalism]; > s.a. Trajectories [quantum states as ensembles of trajectories].
@ Other topics: Halliwell PRD(93)qp, PRD(93)qp [and the uncertainty principle]; Diósi et al PRL(95) [and quantum state diffusion]; Omnès FP(95) [epistemology]; Savvidou JMP(99)gq/98 [action operator]; Clarke qp/00; Halliwell qp/01-in [and spacetime conditions]; Griffiths PRA(02)qp [relativistic, and paradoxes]; Bosse & Hartle PRA(05)qp [spacetime alternatives for operators]; Hartle PRA(08)-a0801 [and extended probabilities]; > s.a. generalized bell inequalities; quantum effects [time of arrival]; wave function collapse.

Decoherent Histories > s.a. decoherence; entropy; relationship classical-quantum mechanics.
* Idea: Environmental noise furnishes the inevitable dephasing that collapses the wave function.
@ General references: Halliwell NYAS(95)gq/94, PRD(98)qp [hydrodynamic-type variables], PRD(01)qp/00; Hartle et al PRD(95)gq/94 [closed systems, conservation laws]; Halliwell QIP-a0904; Gell-Mann & Hartle PRA(12)-a1106 [with one "real" fine-grained history].
@ Decoherence conditions: Scherer et al PLA(04)qp [arbitrarily long histories]; Wallden IJTP(08)gq/06 [spacetime coarse-grainings].
@ Types of theories: Halliwell & Wallden PRD(06)gq/05 [reparametrization-invariant]; > s.a. parametrized theories.
> Gravity-related theories: see FLRW quantum cosmology; minisuperspace quantum cosmology; spin networks; time in quantum gravity.

Coevent Formulation > s.a. measure theory [quantum measures].
@ References: Wallden JPCS(13)-a1301; Ghazi-Tabatabai a1303 [coevents as beables, and topos theory]; Ghazi-Tabatabai a1306 [in terms of truth valuations].

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