S-Matrix for AdS from General Boundary QFT

Colosi, Daniele; Dohse, Max; Oeckl, Robert

doi:10.1088/1742-6596/360/1/012012

Cited by 13 publications

(21 citation statements)

References 6 publications

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“…In particular in Minkowski spacetime, a so-called hypercylinder region, namely a three-ball in space extended over all of time, was considered in [11,12] and the asymptotic amplitude of states defined on the boundary of the hypercylinder was shown to correspond to the standard S-matrix in Minkowski. An analogous hypercylinder region was the basis for proposing an S-matrix for spatially asymptotic states in AdS, [13,14].…”

Section: Introductionmentioning

confidence: 99%

In–out propagator in de Sitter space from general boundary quantum field theory

Colosi¹

2015

Physics Letters B

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The general boundary formulation of quantum theory is applied to quantize a real massive scalar field in de Sitter space. The space-time region where the dynamics of the field takes place is bounded by one spacelike hypersurface of constant conformal de Sitter time. The computation of the amplitude in the presence of a linear interaction with a source field with compact support in the region considered provides the expression of the Feynman propagator which coincides with the so-called in-out propagator.

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Section: Introductionmentioning

confidence: 99%

In–out propagator in de Sitter space from general boundary quantum field theory

Colosi¹

2015

Physics Letters B

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“…The space of admissible solutions L r in a neighborhood of the hypercylinder of radius r contains a full continuum of solutions. This suggests to build the physical S-matrix in AdS on the asymptotic hypercylinder geometry rather than the conventional asymptotic time-interval geometry [11]. While the requisite classical theory was developed in [13], the main ingredient for quantization is the complex structure.…”

Section: Generalized S-matrixmentioning

confidence: 99%

“…Application of this approach to de Sitter spacetime [8,9] and discussion for a larger class of curved spacetimes followed [10]. The application to AdS was outlined in [11], based precisely on the observation that in AdS the hypercylinder geometry is a much more appropriate home for asymptotic free states than the early and late equal-time hypersurfaces of the conventional S-matrix. The present paper is dedicated to a realization of this application to AdS.…”

Section: Introductionmentioning

confidence: 99%

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Complex structures for an S -matrix of Klein–Gordon theory on AdS spacetimes

Dohse¹,

Oeckl²

2015

Class. Quantum Grav.

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While the standard construction of the S-matrix fails on Anti-de Sitter (AdS) spacetime, a generalized S-matrix makes sense, based on the hypercylinder geometry induced by the boundary of AdS. In contrast to quantum field theory in Minkowski spacetime, there is not yet a standard way to resolve the quantization ambiguities arising in its construction. These ambiguities are conveniently encoded in the choice of a complex structure. We explore in this paper the space of complex structures for real scalar Klein-Gordon theory based on a number of criteria. These are: invariance under AdS isometries, induction of a positive definite inner product, compatibility with the standard S-matrix picture and recovery of standard structures in Minkowski spacetime under a limit of vanishing curvature. While there is no complex structure that satisfies all demands, we emphasize two interesting candidates that satisfy most: In one case we have to give up part of the isometry invariance, in the other case the induced inner product is indefinite. * max/robert@matmor.unam.mx arXiv:1501.04667v1 [hep-th]

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“…States on the hypercylinder (belonging to the Hilbert space associated to the hypercylinder hypersurface) are defined for all of times. Moreover, the connectedness of the hypersurface prevents an a priori a The same hypercylinder region considered in Anti-de Sitter space was used to propose a solution to the problem of defining the S-matrix of a field in Anti-de Sitter space where the lack of temporal asymptotic regions prevents the standard construction of the in− and out−states 6,7 . The Fourteenth Marcel Grossmann Meeting Downloaded from www.worldscientific.com by 34.218.44.141 on 05/13/18.…”

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confidence: 99%

General boundary treatment of the Unruh effect

Colosi¹

2017

The Fourteenth Marcel Grossmann Meeting

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The general boundary formulation (GBF) of quantum theory is a new axiomatic formulation that has emerged as a powerful tool to describe the dynamics of quantum fields. Within the GBF we consider the Unruh effect by studying the relation between the quantum field theories of a massive scalar field in 2d Minkowski and Rindler spaces. In particular we underline the existence of an obstruction in the identification of the usual Minkowski vacuum state with a superposition of multiparticle states defined in Rindler space. However, we show that these two states can be related by comparing expectation values of Weyl observables with compact support on the right wedge of Minkowski space. Finally, the quantum state in Rindler space responsible for this local version of the Unruh effect results to be unique.Keywords: Unruh effect; general boundary formulation.The general boundary formulation (GBF) of quantum theory represents an extension of the standard formulation; it is based on two main ingredients: The mathematical framework of Topological Quantum Field Theory (TQFT) and a generalization of the Born rule providing the probability interpretation 1,2 . As in TQFT, a set of axioms associates algebraic structures to geometric ones. In particular, state spaces (usually Hilbert spaces) are defined on hypersurfaces, i.e. oriented manifold of dimension d − 1, and amplitude maps are associated to space-time region, i.e. oriented manifold of dimension d, with boundaries. Such amplitude maps generalize the standard notion of transition amplitudes, usually defined for space-time regions bounded by Cauchy surfaces (in particular, by the disjoint union of an initial Cauchy surface and a final one). In the GBF, the boundary of the region where dynamics takes place is not required to be given by (the disjoint union of) Cauchy surfaces. Arbitrary hypersurfaces are admissible boundaries. For example, in Minkowski space a timelike connected hypersurface given by an hypercylinder (namely, a three ball in space extended over all of times) was considered in Ref. 3. The general interacting theory of a massive Klein-Gordon field defined in the hypercylinder region was shown to be equivalent with the one considered in the region bounded by two equal-Minkowski-time hyperplanes 4,5,a . In the hypercylinder region dynamics is not described in terms of an evolution from an initial state of the system defined at initial time to a final state at a final time. States on the hypercylinder (belonging to the Hilbert space associated to the hypercylinder hypersurface) are defined for all of times. Moreover, the connectedness of the hypersurface prevents an a priori a The same hypercylinder region considered in Anti-de Sitter space was used to propose a solution to the problem of defining the S-matrix of a field in Anti-de Sitter space where the lack of temporal asymptotic regions prevents the standard construction of the in− and out−states 6,7 . The Fourteenth Marcel Grossmann Meeting Downloaded from www.worldscientific.com by 34.218.44.141 on 05/13/18....

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S-Matrix for AdS from General Boundary QFT

Cited by 13 publications

References 6 publications

In–out propagator in de Sitter space from general boundary quantum field theory

In–out propagator in de Sitter space from general boundary quantum field theory

Complex structures for an S -matrix of Klein–Gordon theory on AdS spacetimes

General boundary treatment of the Unruh effect

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