{"arxiv_id":"1306.3575","incoming":{"papers":7,"sentences":14,"groups":[{"kind":"supports_this_paper","label":"Cites it as support","papers":2,"sentences":3,"quotes":[{"arxiv_id":"1711.01067","title":"Quantum de Sitter-black hole in ambient space formalism","url":"/paper/1711.01067","section":"Unitary irreducible representation and Hilbert space","sentence":"Thus the entropy for this Hilbert spaces is finite [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"1403.1204","title":"Quantum Field Theory in de Sitter Universe: Ambient Space Formalism","url":"/paper/1403.1204","section":"Conclusion and outlook","sentence":"As a direct consequence, the total number of quantum states in the Hilbert space turns out to be finite physically [ref] .","intent_p":0.98,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1811.03854","title":"Conjugate spinor field equation for massless spin-$\\frac{3}{2}$ field in de Sitter ambient space","url":"/paper/1811.03854","section":"Introduction","sentence":"Therefore, quantum field theory and gauge theory are investigated in this space-time [ref] .","intent_p":0.9,"contests_p":null}]}],"unlabelled_sentences":10},"outgoing":{"papers":63,"sentences":105,"groups":[{"kind":"method_or_tool","label":"Uses the method or tool of","papers":4,"sentences":4,"quotes":[{"arxiv_id":"math-ph/0311052","title":"Fourier analysis and holomorphic decomposition on the one-sheeted hyperboloid","url":"/paper/math-ph/0311052","section":"Massive scalar field: plane waves","sentence":"By using the Bros-Fourier transformation [ref] , the quantum field operator in this notation is given by: [equation] . +a^†(ξ_T,ν)[(x.ξ_T)_+^-3/2+iν +e^iπ(-3/2+iν)(x.ξ_T)_-^-3/2+iν] }dμ(ξ_T),where $(x·ξ)_+={[ 0 x·ξ≤0; (x·ξ) x·ξ>0; ] .$ [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"gr-qc/9511019","title":"Two-point Functions and Quantum Fields in de Sitter Universe","url":"/paper/gr-qc/9511019","section":"Massive scalar field: plane waves","sentence":"The annihilation operator $a(ξ,ν)$ is a homogeneous function with degree $-3/2+iν$ a̱(ζξ_T,ν)=ζ^-3/2+iνa(ξ_T,ν).Here $T$ stands for an orbital basis of $C^+$. $dμ_T(ξ)$ is an invariant measure defined by [equation] where $i_Ξw_C^+$ denotes the $3$-form on $C^+$ obtained from the contraction of the vector field $Ξ$ with the volume form [equation] Bros et al. have presented two orbital basis [ref] ; the hyperbolic-type sub-manifold $T_4=T_4^+ ∪T_4^-$ defined by Ṯ^±_4={ ξ∈C^+; ξ^4=±m_H},which is invariant under $SO(1,3)$ group, and the spherical-type submanifold $T_0$ defined by Ṯ_0={ ξ∈C^+; ξ^0=m_H>0, ξ⃗.ξ⃗+ (ξ^4)^2= m_H^2},which is invariant under $SO(4)$ group.","intent_p":0.97,"contests_p":null},{"arxiv_id":"hep-th/0110007","title":"Les Houches Lectures on De Sitter Space","url":"/paper/hep-th/0110007","section":"Entropy in de Sitter space-time","sentence":"Gibbons and Hawking have suggested to use the following relation [ref] : ḏ(-E)=TdS,instead of the equation ([ref]), and then we obtain: E̱=μ/π arctan( H/μ)=μ/π arctan( 2πT/μ).In the null curvature limit we have $(H=0=T)$, E̱=μ/π ∑_n^∞(-1)^n/2n+1( 2πT/μ)^2n+1=2T-μ/3( 2πT/μ)^3+... .In this limit, we obtain $E=0$, which is a logical result!","intent_p":0.84,"contests_p":null},{"arxiv_id":"1403.1204","title":"Quantum Field Theory in de Sitter Universe: Ambient Space Formalism","url":"/paper/1403.1204","section":"Entropy in de Sitter space-time","sentence":"The interaction is reformulated in ambient space formalism by using the gauge principle [ref] .","intent_p":0.99,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites as support","papers":3,"sentences":3,"quotes":[{"arxiv_id":"gr-qc/9511019","title":"Two-point Functions and Quantum Fields in de Sitter Universe","url":"/paper/gr-qc/9511019","section":"Massive scalar field: plane waves","sentence":"These two Hilbert spaces $H_T_0$ and $H_T_4$, are unitary equivalent [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"0903.2670","title":"Linear Weyl Gravity in de Sitter Universe","url":"/paper/0903.2670","section":"Entropy in de Sitter space-time","sentence":"From the group theoretical point of view it is proved that the second part cannot be described by a rank-$2$ symmetric tensor field in the ambient space notation or Dirac $6$-cone formalism [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"0903.5249","title":"Conformal linear gravity in de Sitter space","url":"/paper/0903.5249","section":"Entropy in de Sitter space-time","sentence":"From the group theoretical point of view it is proved that the second part cannot be described by a rank-$2$ symmetric tensor field in the ambient space notation or Dirac $6$-cone formalism [ref] .","intent_p":0.98,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":18,"sentences":21,"quotes":[{"arxiv_id":"gr-qc/9511019","title":"Two-point Functions and Quantum Fields in de Sitter Universe","url":"/paper/gr-qc/9511019","section":"Massive scalar field: plane waves","sentence":"Details can be found in [ref] .","intent_p":0.87,"contests_p":null},{"arxiv_id":"hep-th/9806100","title":"Masslessness in $n$-dimensions","url":"/paper/hep-th/9806100","section":"Discrete UIR of the conformal group","sentence":"In the previous works, a variety of realizations of the conformal group UIRs and their corresponding Hilbert spaces have been constructed [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1210.6348","title":"Black Holes, Information, and Hilbert Space for Quantum Gravity","url":"/paper/1210.6348","section":"Introduction","sentence":"These problems have been surveyed in different methods by several authors [ref] .","intent_p":0.96,"contests_p":null},{"arxiv_id":"1210.7244","title":"Entanglement entropy in de Sitter space","url":"/paper/1210.7244","section":"Introduction","sentence":"These problems have been surveyed in different methods by several authors [ref] .","intent_p":0.96,"contests_p":null},{"arxiv_id":"1301.3387","title":"Near-Extremal Vanishing Horizon AdS5 Black Holes and Their CFT Duals","url":"/paper/1301.3387","section":"Introduction","sentence":"These problems have been surveyed in different methods by several authors [ref] .","intent_p":0.96,"contests_p":null}]}],"unlabelled_sentences":77},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/1306.3575"}}