Perturbative Algebraic Quantum Field Theory

Rejzner, Kasia

doi:10.1007/978-3-319-25901-7

Cited by 96 publications

(59 citation statements)

References 29 publications

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“…2.3]), as this is an interacting theory problem. For addressing such a matter, perhaps modern techniques of perturbation theory in curved spacetimes should be useful [17].…”

Section: Casementioning

confidence: 99%

Semi-classical gravity in de Sitter spacetime and the cosmological constant

Juárez-Aubry

2019

Physics Letters B

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We show that there exist solutions to the semi-classical gravity equations in de Sitter spacetime sourced by the renormalised stress-energy tensor of a free Klein-Gordon field. For the massless scalar, solutions exist for every possible value of the cosmological constant, provided that the curvature coupling parameter is chosen appropriately. In the massive case, imposing Wald's axioms for the renormalised stress-energy tensor, the mass of the field and the curvature coupling constraint the allowed values of Λ. For a massive, minimally coupled field, a "small Λ" solution is found, fixed by the relation m 2 ≃ 4.89707 × 10 12 Λ. We emphasise that in this framework, the old cosmological constant problem in its standard formulation plays no rôle, in the sense that there are no bare-vs-physical values of Λ, for only the physical Λ appears in the semi-classical equations, and the value that it is allowed to take is fixed or restricted by the equations themselves. We explain that there is an important relation between the cosmological constant problem and the violation of Wald's stress-energy renormalisation axioms.

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“…2.3]), as this is an interacting theory problem. For addressing such a matter, perhaps modern techniques of perturbation theory in curved spacetimes should be useful [17].…”

Section: Casementioning

confidence: 99%

Semi-classical gravity in de Sitter spacetime and the cosmological constant

Juárez-Aubry

2019

Physics Letters B

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“…In the framework of pAQFT interacting fields are constructed with the use of the Bogoliubov formula [BS59,DF01a] (see also [Rej16] for a review)…”

Section: Interacting Fieldsmentioning

confidence: 99%

The Quantum Sine-Gordon Model in Perturbative AQFT

Bahns

Rejzner²

2017

Commun. Math. Phys.

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Abstract:We study the Sine-Gordon model with Minkowski signature in the framework of perturbative algebraic quantum field theory. We calculate the vertex operator algebra braiding property. We prove that in the finite regime of the model, the expectation valuewith respect to the vacuum or a Hadamard state-of the Epstein Glaser S-matrix and the interacting current or the field respectively converge, both given as formal power series.

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“…holds -this can be checked in examples but is expected on the basis e.g., of Bogoliubov's factorisation formula in perturbative QFT [24,11,4]. Note that the mapΘ 2 appears to the right because our scattering morphisms map from the future to the past.…”

Section: Instruments and Change Of Statementioning

confidence: 87%

“…is the post-selected system state after selective measurement of the probe.1 The term 'post-selection' is used in various ways in the literature; to be clear, the meaning intended here is given by (24), i.e., the post-selected state is the one in which the probability of observing a system effect A is equal to the conditional probability, in the original state, of observing A given that the probe effect is observed.…”

Section: Instruments and Change Of Statementioning

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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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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Perturbative Algebraic Quantum Field Theory

Cited by 96 publications

References 29 publications

Semi-classical gravity in de Sitter spacetime and the cosmological constant

Semi-classical gravity in de Sitter spacetime and the cosmological constant

The Quantum Sine-Gordon Model in Perturbative AQFT

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

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