Algebraic Quantum Field Theory in Curved Spacetimes

Fewster, Christopher J.; Verch, Rainer

doi:10.1007/978-3-319-21353-8_4

Cited by 60 publications

(96 citation statements)

References 195 publications

(442 reference statements)

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“…To each such spacetime M, we assume that such the QFT is Comparing with assumptions standard in flat spacetime (see, e.g., [12]) one notes that Poincaré covariance has been replaced by the compatibility condition. What we have described is a cut-down version of locally covariant QFT [6,15], the full version of which would describe the theory as a functor from the category of globally hyperbolic spacetimes to a category of unital * -algebras. Einstein causality may be built in by suitable monoidal [5] or operadic [3] refinements.…”

Section: System Probe and Couplingmentioning

confidence: 99%

“…In short, this definition asserts that the theories U and C coincide outside the causal hull of K, capturing the idea that the coupling is only switched on in this region. There is a close link to the discussion of equivalence between theories in local covariant QFT [6,14,15]. Many properties of the coupling can be described in terms of a scattering map defined as follows.…”

Section: System Probe and Couplingmentioning

confidence: 99%

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A Generally Covariant Measurement Scheme for Quantum Field Theory in Curved Spacetimes

Fewster

2020

Progress and Visions in Quantum Theory in View of Gravity

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We propose and develop a measurement scheme for quantum field theory (QFT) in curved spacetimes, in which the QFT of interest, the "system", is dynamically coupled to another, the "probe", in a compact spacetime region. Measurements of observables in the probe system then serve as proxy measurements of observables in the system, under a correspondence which depends also on a preparation state of the probe theory. All our constructions are local and covariant, and the conditions may be stated abstractly in the framework of algebraic quantum field theory (AQFT). The induced system observables corresponding to probe observables may be localized in the causal hull of the coupling region and are typically less sharp than the probe observable, but more sharp than the actual measurement on the coupled theory. A formula is given for the post-selected system state, conditioned on measurement outcomes, which is closely related to the notion of an instrument as introduced by Davies and Lewis. This formula has the important property that individual measurements form consistent composites, provided that their coupling regions can be causally ordered and a certain causal factorisation property holds for the dynamics; the composite is independent of the causal order chosen if more than one exists. The general framework is amenable to calculation, as is shown in a specific example. This contribution reports on joint work with R. Verch, arXiv:1810.06512. IntroductionA typical first course on quantum mechanics will include some straightforward rules describing measurements. It might be said, for example, that an ideal measurement of a quantum mechanical observable returns one of the eigenvalues of the operator representing the observable, and the system is to be found in the corresponding CJ Fewster

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Section: System Probe and Couplingmentioning

confidence: 99%

Section: System Probe and Couplingmentioning

confidence: 99%

A Generally Covariant Measurement Scheme for Quantum Field Theory in Curved Spacetimes

Fewster

2020

Progress and Visions in Quantum Theory in View of Gravity

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“…In fact there is reason to assume that every physically realistic QFT on a globally hyperbolic spacetime complies with this basic structure. (See [14] for discussion. )…”

Section: Relativistic Quantum Field Theorymentioning

confidence: 99%

The D-CTC Condition in Quantum Field Theory

Verch

2020

Progress and Visions in Quantum Theory in View of Gravity

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A condition proposed by David Deutsch to describe analogues of processes in the presence of closed timelike curves (D-CTC condition) in bipartite quantum systems is investigated within the framework of local relativistic quantum field theory. The main result is that in relativistic quantum field theory on spacetimes where closed timelike curves are absent, the D-CTC condition can nevertheless be fulfilled to arbitrary precision, under very general, model-independent conditions. Therefore, the D-CTC condition should not be taken as characteristic for quantum processes in the presence of closed timelike curves in the sense of general relativity. This report is a very condensed extract of the publication [35]. A new result showing that the D-CTC condition can be approximately fulfilled by entangled states is also presented.

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“…Nowadays regarded as an indispensable ingredient in the perturbative construction of interacting fields (see e.g. recent reviews [HW3,KM,FV2]), this property accounts for the correct short-distance behaviour of two-point functions. It can be conveniently formulated as a condition on the wave front set of the state's two-point functions [Ra] -a terminology that we explain in the paragraphs below.…”

mentioning

confidence: 99%

“…The importance of Hadamard states is primarily due to their pivotal role in renormalization on curved spacetimes [BF2,HW1,HW2,Da], see [FV2,KM,HW3] for recent reviews.…”

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confidence: 99%