Algebraic approach to quantum field theory on non-globally-hyperbolic spacetimes

Yurtsever, Ulvi

doi:10.1088/0264-9381/11/4/016

Cited by 20 publications

(48 citation statements)

References 6 publications

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“…In this way we have performed a complete characterization of P-CTC in the most commonly employed frameworks for quantum mechanics, with the exception of algebraic methods (e.g. see [62]). …”

Section: Discussionmentioning

confidence: 99%

Quantum mechanics of time travel through post-selected teleportation

et al. 2011

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This paper discusses the quantum mechanics of closed timelike curves (CTCs) and of other potential methods for time travel. We analyze a specific proposal for such quantum time travel, the quantum description of CTCs based on post-selected teleportation (P-CTCs). We compare the theory of P-CTCs to previously proposed quantum theories of time travel: the theory is physically inequivalent to Deutsch's theory of CTCs, but it is consistent with path-integral approaches (which are the best suited for analyzing quantum field theory in curved spacetime). We derive the dynamical equations that a chronology-respecting system interacting with a CTC will experience. We discuss the possibility of time travel in the absence of general relativistic closed timelike curves, and investigate the implications of P-CTCs for enhancing the power of computation.

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Section: Discussionmentioning

confidence: 99%

Quantum mechanics of time travel through post-selected teleportation

et al. 2011

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“…Our argument consists of two steps. First, consider a bisolution Γ ∈ W (2) g (g ∈ G K ) which is locally causal with respect to C + g (standing for either C T + g or C S+ g ). We will show that the local causality of Γ implies that the bisolutions Γ ± for P η with which Γ agrees in M ± × M ± are both translationally invariant, in the sense that…”

Section: Locally Causal Bisolutions On Mmentioning

confidence: 99%

“…The result does not hold if µ = 0 (the requirement that µ is not a negative integer is included for technical convenience). Now translational invariance of a bisolution Γ 0 ∈ W (2) η entails that in the expansion with polynomially bounded coefficients γ nǫ and γ nǫ . But we also have…”

Section: Locally Causal Bisolutions On Mmentioning

confidence: 99%

Bisolutions to the Klein-Gordon equation and quantum field theory on two-dimensional cylinder spacetimes

Fewster¹

1999

Class. Quantum Grav.

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We consider 2-dimensional cylinder spacetimes whose metrics differ from the flat Minkowskian metric within a compact region K. By choice of time orientation, these spacetimes may be regarded as either globally hyperbolic timelike cylinders or nonglobally hyperbolic spacelike cylinders. For generic metrics in our class, we classify all possible candidate quantum field algebras for massive Klein-Gordon theory which obey the F-locality condition introduced by Kay. This condition requires each point of spacetime to have an intrinsically globally hyperbolic neighbourhood N such that the commutator (in the candidate algebra) of fields smeared with test functions supported in N agrees with the value obtained in the usual construction of Klein-Gordon theory on N .By considering bisolutions to the Klein-Gordon equation, we prove that generic timelike cylinders admit a unique F-local algebra -namely the algebra obtained by the usual construction -and that generic spacelike cylinders do not admit any F-local algebras, and are therefore non F-quantum compatible. Refined versions of our results are obtained for subclasses of metrics invariant under a symmetry group. Thus F-local field theory on 2-dimensional cylinder spacetimes essentially coincides with the usual globally hyperbolic theory. In particular the result of the author and Higuchi that the Minkowskian spacelike cylinder admits infinitely many F-local algebras is now seen to represent an anomalous case. *

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“…This is the case of the definition of a quasi-local algebra [6,15]. However, since here interpretation is the main concern, the full link to spacetime will be required [16,17]. …”

Section: Local Algebras Of Observablesmentioning

confidence: 99%

“…A pleasant feature of the local algebra structure is that the C * -subalgebras A(Ω) (with Ω ∈ M ) of A are actually sufficient to reconstruct the spacetime M as a topological space and to determine its causal structure, as observed by U.Yurtsever [16,17].…”

Section: For Any Collection {ω I } Of Open Subsets Of M One Hasmentioning

confidence: 99%

Spectral Geometry and Causality

Kopf

1998

Int. J. Mod. Phys. A

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Abstract. For a physical interpretation of a theory of quantum gravity, it is necessary to recover classical spacetime, at least approximately. However, quantum gravity may eventually provide classical spacetimes by giving spectral data similar to those appearing in noncommutative geometry, rather than by giving directly a spacetime manifold. It is shown that a globally hyperbolic Lorentzian manifold can be given by spectral data. A new phenomenon in the context of spectral geometry is observed: causal relationships. The employment of the causal relationships of spectral data is shown to lead to a highly efficient description of Lorentzian manifolds, indicating the possible usefulness of this approach. Connections to free quantum field theory are discussed for both motivation and physical interpretation. It is conjectured that the necessary spectral data can be generically obtained from an effective field theory having the fundamental structures of generalized quantum mechanics: a decoherence functional and a choice of histories.

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Algebraic approach to quantum field theory on non-globally-hyperbolic spacetimes

Cited by 20 publications

References 6 publications

Quantum mechanics of time travel through post-selected teleportation

Quantum mechanics of time travel through post-selected teleportation

Bisolutions to the Klein-Gordon equation and quantum field theory on two-dimensional cylinder spacetimes

Spectral Geometry and Causality

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