Conformal extension of the Bunch-Davies state across the de Sitter boundary

Wrochna, Michał

doi:10.1063/1.5023646

Cited by 4 publications

(3 citation statements)

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“…In this picture, the splitting of the radial sets at infinity into sinks and sources plays the rôle of the asymptotic decomposition into particles and anti-particles. Similar arguments have also been applied to asymptotically de Sitter spaces (the Lorentzian analogue of asymptotically hyperbolic spaces) [GHV16,Va17,VW18,Wr19].…”

Section: Introduction and Main Resultsmentioning

confidence: 95%

The Feynman problem for the Klein–Gordon equation

Gérard¹,

Wrochna²

2022

Séminaire Laurent Schwartz — EDP Et Applications

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Section: Introduction and Main Resultsmentioning

confidence: 95%

The Feynman problem for the Klein–Gordon equation

Gérard¹,

Wrochna²

2022

Séminaire Laurent Schwartz — EDP Et Applications

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“…(17.24)). 87 [Again, the full Hilbertian Fock space H of the theory is given by the Hilbertian sum H 0 ⊕ ⊕ n S(H 1 ) ⊗n .] As a matter of fact, any ḟ1 ∈ H 1 corresponds to a function f 1 (x) which, with respect to the Fourier transform (16.10), is determined by:…”

Section: Plane-wave Analysis Of the Two-point Functionsmentioning

confidence: 99%

“…The dS 4 (generally, dS d ) plane waves are also of great significance in constructing possible models of dS 4 /CFT 3 (generally, dS d /CFT d−1 ) correspondence. For this case, which is beyond the scope of this paper, readers are referred to Refs [87][88][89]…”

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confidence: 99%

The de Sitter group and its representations: a window on the notion of de Sitterian elementary systems

Enayati,

Gazeau,

Pejhan

et al. 2022

Preprint

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We review the construction of ("free") elementary systems in de Sitter (dS) spacetime, in the Wigner sense, as associated with unitary irreducible representations (UIR's) of the dS (relativity) group. This study emphasizes the conceptual issues arising in the formulation of such systems and discusses known results in a mathematically rigorous way. Particular attention is paid to: "smooth" transition from classical to quantum theory; physical content under vanishing curvature, from the point of view of a local ("tangent") Minkowskian observer; and thermal interpretation (on the quantum level), in the sense of the Gibbons-Hawking temperature. We review three decompositions of the dS group physically relevant for the description of dS spacetime and classical phase spaces of elementary systems living on it. We review the construction of (projective) dS UIR's issued from these group decompositions. (Projective) Hilbert spaces carrying the UIR's (in some restricted sense) identify quantum ("one-particle") states spaces of dS elementary systems. Adopting a well-established Fock procedure, based on the Wightman-Gärding axiomatic and on analyticity requirements in the complexified Riemannian manifold, we proceed with a consistent quantum field theory (QFT) formulation of elementary systems in dS spacetime. This dS QFT formulation closely parallels the corresponding Minkowskian one, while the usual spectral condition is replaced by a certain geometric Kubo-Martin-Schwinger (KMS) condition equivalent to a precise thermal manifestation of the associated "vacuum" states. We end our study by reviewing a consistent and univocal definition of mass in dS relativity. This definition, presented in terms of invariant parameters characterizing the dS UIR's, accurately gives sense to terms like "massive" and "massless" fields in dS relativity according to their Minkowskian counterparts, yielded by the group contraction procedures. Contents

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