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 Copenhagen one, and more realist.

References > s.a. formulations of quantum mechanics; path-integral formulation.
@ General: Gell-Mann & Hartle in(90); Hartle ViA(93)gq/92; Gell-Mann & Hartle PRD(93)gq, 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 gq/99-PhD [continuous time]; Brun qp/03-in [resolving ambiguities]; Sorkin JPA(07)qp/06; Henson JPCS(09)-a0901 [and correspondence principle].
@ Reviews: Halliwell gq/93-in, qp/03-in; Dowker & Kent JSP(96)gq/94; Kent PS(98)gq; Griffiths & Omnès PT(99)aug; Griffiths 01; Dass qp/05-ln; Chisholm qp/06-in; Hohenberg a0909 [intro].
@ 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.
@ Decoherence functionals: Isham & Linden JMP(94)gq; Isham et al JMP(94)gq.
@ Continuous: Isham & Linden JMP(95)gq; Isham et al JMP(98)qp/97; Anastopoulos JMP(01)qp/00; Kouletsis gq/01-PhD.
@ Generalized: Isham JMP(94)gq/93, qp/95, IJTP(97)gq/96, Pulmannová IJTP(95) [algebraic formulation, logic, topos theory]; Goldstein & Page PRL(95); Rudolph IJTP(96)qp/95, JMP(98); Raptis qp/01 [topos-theoretic].
@ 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].
@ Problems: Peruzzi & Rimini FPL(98)qp/97; Bassi & Ghirardi JSP(00)qp/99 [and realism], reply Griffiths JSP(00)qp; Nisticò PE(03)qp.
@ 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).
@ Other systems and topics: Griffiths qp/95, qp/96 [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; logic [anhomomorphic logic]; Trajectories.
@ 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]; > 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]; Burch JMP(07)qp [perturbation theory, oscillator].
@ Quantum measure theory: Dowker & Ghazi-Tabatabai JPA(08)-a0712 [dynamical wave-function-collapse models]; > s.a. measure theory.
@ 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]; Raptis et al IJTP(07) [tomographic histories representation]; Hartle PRA(08)-a0801 [and extended probabilities].

Decoherent Histories > s.a. decoherence; entropy; time in quantum gravity.
* 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 a0904/QIP.
@ 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.

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