The Time Slice Axiom in Perturbative Quantum Field Theory on Globally Hyperbolic Spacetimes

Chilian, Bruno; Fredenhagen, Klaus

doi:10.1007/s00220-008-0670-7

Cited by 47 publications

(82 citation statements)

References 21 publications

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“…Our general argument shows that the association of a cobordism between two Cauchy surfaces of globally hyperbolic spacetimes to an isomorphism of algebras always exists provided the time slice axiom is satisfied. As recently shown, the latter axiom is actually generally valid in perturbative Algebraic Quantum Field Theory [13].…”

Section: Locally Covariant Field Theorymentioning

confidence: 82%

Perturbative Algebraic Quantum Field Theory

Rejzner¹

2016

Mathematical Physics Studies

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Section: Locally Covariant Field Theorymentioning

confidence: 82%

Perturbative Algebraic Quantum Field Theory

Rejzner¹

2016

Mathematical Physics Studies

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“…In either case the idea is to show that the algebra generated by local operators on a time-slice acts irreducibly on the Hilbert space; the statement then follows from Schur's lemma. In the continuum this idea is called the "time-slice axiom" [3,4]; for recent rigorous discussions, see, e.g., [5,6]. There are actually topological theories where the time-slice axiom is false, for example in Chern-Simons theory quantized on a topologically nontrivial Riemann surface, but we don't expect this loophole to be relevant for CFTs with ordinary gravity duals.…”

Section: Jhep04(2015)163mentioning

confidence: 99%

Bulk locality and quantum error correction in AdS/CFT

Almheiri

Dong

Harlow

2015

J. High Energ. Phys.

704

1,132

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We point out a connection between the emergence of bulk locality in AdS/CFT and the theory of quantum error correction. Bulk notions such as Bogoliubov transformations, location in the radial direction, and the holographic entropy bound all have natural CFT interpretations in the language of quantum error correction. We also show that the question of whether bulk operator reconstruction works only in the causal wedge or all the way to the extremal surface is related to the question of whether or not the quantum error correcting code realized by AdS/CFT is also a "quantum secret sharing scheme", and suggest a tensor network calculation that may settle the issue. Interestingly, the version of quantum error correction which is best suited to our analysis is the somewhat nonstandard "operator algebra quantum error correction" of Beny, Kempf, and Kribs. Our proposal gives a precise formulation of the idea of "subregion-subregion" duality in AdS/CFT, and clarifies the limits of its validity.

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“…We can fix this ambiguity by fixing the expectation value for any given but fixed m = m 0 , L = L 0 . If one is considering a scalar field of mass m 0 , the usual choice of c 2 would be c 2 = log m 2 0 /16π 2 , so that 20 lim L→∞ ω 0 (φ 2 ) = 0. Once c 2 has been chosen, the expectation value of φ 2 is uniquely determined for any other m, L, and in fact for any other state, such as a finite temperature state.…”

Section: Construction Of Nonlinear Observables For a Free Quantum Scamentioning

confidence: 99%

Quantum Fields in Curved Spacetime

Hollands¹,

Wald²

2015

General Relativity and Gravitation

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We review the theory of quantum fields propagating in an arbitrary, classical, globally hyperbolic spacetime. Our review emphasizes the conceptual issues arising in the formulation of the theory and presents known results in a mathematically precise way. Particular attention is paid to the distributional nature of quantum fields, to their local and covariant character, and to microlocal spectrum conditions satisfied by physically reasonable states. We review the Unruh and Hawking effects for free fields, as well as the behavior of free fields in deSitter spacetime and FLRW spacetimes with an exponential phase of expansion. We review how nonlinear observables of a free field, such as the stress-energy tensor, are defined, as well as timeordered-products. The "renormalization ambiguities" involved in the definition of time-ordered products are fully characterized. Interacting fields are then perturbatively constructed. Our main focus is on the theory of a scalar field, but a brief discussion of gauge fields is included. We conclude with a brief discussion of a possible approach towards a nonperturbative formulation of quantum field theory in curved spacetime and some remarks on the formulation of quantum gravity. Quantum field theory in curved spacetime (QFTCS) is the theory of quantum fields propagating in a background, classical, curved spacetime (M , g). On account of its classical treatment of the metric, QFTCS cannot be a fundamental theory of nature. However, QFTCS is expected to provide an accurate description of quantum phenomena in a regime where the effects of curved spacetime may be significant, but effects of quantum gravity itself may be neglected. In particular, it is expected that QFTCS should be applicable to the description of quantum phenomena occurring in the early universe and near (and inside of) black holesprovided that one does not attempt to describe phenomena occurring so near to singularities that curvatures reach Planckian scales and the quantum nature of the spacetime metric would have to be taken into account.It should be possible to derive QFTCS by taking a suitable limit of a more fundamental theory wherein the spacetime metric is treated in accord with the principles of quantum theory. However, this has not been done-except in formal and/or heuristic ways-simply because no present quantum theory of gravity has been developed to the point where such a well defined limit can be taken. Rather, the framework of QFTCS that we shall describe in this review has been obtained by suitably merging basic principles of classical general relativity with the basic principles of quantum field theory in Minkowski spacetime. As we shall explain further below, the basic principles of classical general relativity are relatively easy to identify and adhere to, but it is far less clear what to identify as the "basic principles" of quantum field theory in Minkowski spacetime. Indeed, many of the concepts normally viewed as fundamental to quantum field theory in Minkowski spacetime, such as Poinca...

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The Time Slice Axiom in Perturbative Quantum Field Theory on Globally Hyperbolic Spacetimes

Cited by 47 publications

References 21 publications

Perturbative Algebraic Quantum Field Theory

Perturbative Algebraic Quantum Field Theory

Bulk locality and quantum error correction in AdS/CFT

Quantum Fields in Curved Spacetime

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