On the algebraic quantization of a massive scalar field in anti-de Sitter spacetime

Dappiaggi, Claudio; Ferreira, Hugo R. C.

doi:10.1142/s0129055x18500046

Cited by 23 publications

(34 citation statements)

References 36 publications

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“…We shall illustrate this fact by using the free Klein-Gordon theory as an example. Thus, our results also provide a bridge between the ideas of [30] and the concrete constructions in [8,[10][11][12].…”

Section: Introductionsupporting

confidence: 62%

“…For specific choices of boundary conditions, there exist successful constructions of algebraic quantum field theories on spacetimes with timelike boundary, see e.g., [8,[10][11][12]. The main message of these works is that the algebraic approach is versatile enough to account also for these models, although some key structures, such as for example the notion of Hadamard states [11,32], should be modified accordingly.…”

Section: Introductionmentioning

confidence: 99%

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Algebraic Quantum Field Theory on Spacetimes with Timelike Boundary

Benini

Dappiaggi

Schenkel

2018

Ann. Henri Poincaré

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Abstract. We analyze quantum field theories on spacetimes M with timelike boundary from a model-independent perspective. We construct an adjunction which describes a universal extension to the whole spacetime M of theories defined only on the interior intM . The unit of this adjunction is a natural isomorphism, which implies that our universal extension satisfies Kay's F-locality property. Our main result is the following characterization theorem: Every quantum field theory on M that is additive from the interior (i.e., generated by observables localized in the interior) admits a presentation by a quantum field theory on the interior intM and an ideal of its universal extension that is trivial on the interior. We shall illustrate our constructions by applying them to the free Klein-Gordon field.

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Section: Introductionsupporting

confidence: 62%

Section: Introductionmentioning

confidence: 99%

Algebraic Quantum Field Theory on Spacetimes with Timelike Boundary

Benini

Dappiaggi

Schenkel

2018

Ann. Henri Poincaré

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“…These boundary conditions appear frequently in the physics literature; see e.g. [DF2,DFM]. Further motivation comes from the study of the Dirichlet-to-Neumann operator, which was recently shown to coincide with a power of the wave operator in the case of a static metric [EdMGV].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

PROPAGATION OF SINGULARITIES ON AdS SPACETIMES FOR GENERAL BOUNDARY CONDITIONS AND THE HOLOGRAPHIC HADAMARD CONDITION

Gannot¹,

Wrochna²

2020

J. Inst. Math. Jussieu

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We consider the Klein-Gordon equation on asymptotically anti-de Sitter spacetimes subject to Neumann or Robin (or Dirichlet) boundary conditions, and prove propagation of singularities along generalized broken bicharacteristics. The result is formulated in terms of conormal regularity relative to a twisted Sobolev space. We use this to show the uniqueness, modulo regularising terms, of parametrices with prescribed b-wavefront set. Furthermore, in the context of quantum fields, we show a similar result for two-point functions satisfying a holographic Hadamard condition on the b-wavefront set.

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“…To answer this question we follow the same procedure as in [8][9][10] which relies on Sturm-Liouville theory for ordinary differential equations. A reader interested in more details can consult [18] on which we base our analysis.…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…The techniques used in [8] are rather flexible; they have been studied from a rigorous viewpoint in [9] and applied also to the analysis of a Klein-Gordon field in BTZ spacetime in [10]. In this paper, first we also apply them to the study of a massive, real scalar field in the global chart of CAdS n , in order to investigate if the results obtained in the Poincaré patch do extend globally.…”

Section: Introductionmentioning

confidence: 99%

Ground states of a Klein-Gordon field with Robin boundary conditions in global anti–de Sitter spacetime

2018

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We consider a real, massive scalar field both on the n-dimensional anti-de Sitter (AdS n ) spacetime and on its universal cover CAdS n . In the second scenario, we extend the recent analysis on PAdS n , the Poincaré patch of AdS n , first determining all admissible boundary conditions of Robin type that can be applied on the conformal boundary. Most notably, contrary to what happens on PAdS n , no bound state mode solution occurs. Subsequently, we address the problem of constructing the two-point function for the ground state satisfying the admissible boundary conditions. All these states are locally of Hadamard form being obtained via a mode expansion which encompasses only the positive frequencies associated to the global timelike Killing field on CAdS n . To conclude we investigate under which conditions any of the two-point correlation functions constructed on the universal cover defines a counterpart on AdS n , still of Hadamard form. Since this spacetime is periodic in time, it turns out that this is possible only for Dirichlet boundary conditions, though for a countable set of masses of the underlying field, or for Neumann boundary conditions, though only for even dimensions and for one given value of the mass.

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On the algebraic quantization of a massive scalar field in anti-de Sitter spacetime

Cited by 23 publications

References 36 publications

Algebraic Quantum Field Theory on Spacetimes with Timelike Boundary

Algebraic Quantum Field Theory on Spacetimes with Timelike Boundary

PROPAGATION OF SINGULARITIES ON AdS SPACETIMES FOR GENERAL BOUNDARY CONDITIONS AND THE HOLOGRAPHIC HADAMARD CONDITION

Ground states of a Klein-Gordon field with Robin boundary conditions in global anti–de Sitter spacetime

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