Entropy of Quantum Fields in de Sitter Space-time

M.V. Takook

RECORD

Entropy of Quantum Fields in de Sitter Space-time

M.V. Takook

General Relativity and Quantum Cosmology · Submitted 15 Jun 2013

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The entropy of the quantum fields on this Hilbert space have been calculated which is finite and invariant for all inertial observers on the de Sitter hyperboloid.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,005 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.16 · compares with prior results 0.06 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

The quantum states or Hilbert spaces for the quantum field theory in de Sitter space-time are studied on ambient space formalism. In this formalism, the quantum states are only depended $(1)$ on the topological character of the de Sitter space-time, {\it i.e.} $\R \times S^3$, and $(2)$ on the homogeneous spaces which are used for construction of the unitary irreducible representation of de Sitter group. A compact homogeneous space is chosen in this paper. The unique feature of this homogeneous space is that its total number of quantum states, ${\cal N}$, is finite although the Hilbert space has infinite dimensions. It is shown that ${\cal N}$ is a continuous function of the Hubble constant $H$ and the eigenvalue of the Casimir operators of de Sitter group. The entropy of the quantum fields on this Hilbert space have been calculated which is finite and invariant for all inertial observers on the de Sitter hyperboloid.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The quantum states or Hilbert spaces for the quantum field theory in de Sitter space-time are studied on ambient space formalism.	contribution 0.73	0.76	0.04	asserted 0.96
s1	In this formalism, the quantum states are only depended $(1)$ on the topological character of the de Sitter space-time, {\it i.e.} $\R \times S^3$, and $(2)$ on the homogeneous spaces which are used for construction of the unitary irreducible representation of de Sitter group.	background 0.54	0.23	0.07	asserted 1.00
s2	A compact homogeneous space is chosen in this paper.	method 0.77	0.90	0.03	asserted 0.99
s3	The unique feature of this homogeneous space is that its total number of quantum states, ${\cal N}$, is finite although the Hilbert space has infinite dimensions.	result 0.53	0.81	0.16	asserted 1.00
s4	It is shown that ${\cal N}$ is a continuous function of the Hubble constant $H$ and the eigenvalue of the Casimir operators of de Sitter group.	result 0.99	0.88	0.15	asserted 1.00
s5	The entropy of the quantum fields on this Hilbert space have been calculated which is finite and invariant for all inertial observers on the de Sitter hyperboloid.	result 1.00	0.91	0.66	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

The quantum states or Hilbert spaces for the quantum field theory in de Sitter space-time are studied on ambient space formalism. In this formalism, the quantum states are only depended $(1)$ on the topological character of the de Sitter space-time, {\it i.e.} $\R \times S^3$, and $(2)$ on the homogeneous spaces which are used for construction of the unitary irreducible representation of de Sitter group. A compact homogeneous space is chosen in this paper. The unique feature of this homogeneous space is that its total number of quantum states, ${\cal N}$, is finite although the Hilbert space has infinite dimensions. It is shown that ${\cal N}$ is a continuous function of the Hubble constant $H$ and the eigenvalue of the Casimir operators of de Sitter group. The entropy of the quantum fields on this Hilbert space have been calculated which is finite and invariant for all inertial observers on the de Sitter hyperboloid.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

7 arXiv papers cite this in 14 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 10 sentences without a confident label

Cites it as support 2 papers

Thus the entropy for this Hilbert spaces is finite [ref] .

Quantum de Sitter-black hole in ambient space formalism · Unitary irreducible representation and Hilbert space · 0.99
As a direct consequence, the total number of quantum states in the Hilbert space turns out to be finite physically [ref] .

Quantum Field Theory in de Sitter Universe: Ambient Space Formalism · Conclusion and outlook · 0.98

Cites it as background 1 paper

Therefore, quantum field theory and gauge theory are investigated in this space-time [ref] .

Conjugate spinor field equation for massless spin-$\frac{3}{2}$ field in de Sitter ambient space · Introduction · 0.90

What it cites · 77 sentences without a confident label

Uses the method or tool of 4 papers

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] .

Fourier analysis and holomorphic decomposition on the one-sheeted hyperboloid · Massive scalar field: plane waves · 1.00
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.

Two-point Functions and Quantum Fields in de Sitter Universe · Massive scalar field: plane waves · 0.97
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!

Les Houches Lectures on De Sitter Space · Entropy in de Sitter space-time · 0.84

Cites as support 3 papers

These two Hilbert spaces $H_T_0$ and $H_T_4$, are unitary equivalent [ref] .

Two-point Functions and Quantum Fields in de Sitter Universe · Massive scalar field: plane waves · 0.99
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] .

Linear Weyl Gravity in de Sitter Universe · Entropy in de Sitter space-time · 0.98
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] .

Conformal linear gravity in de Sitter space · Entropy in de Sitter space-time · 0.98

Cites as background 18 papers

Details can be found in [ref] .

Two-point Functions and Quantum Fields in de Sitter Universe · Massive scalar field: plane waves · 0.87
In the previous works, a variety of realizations of the conformal group UIRs and their corresponding Hilbert spaces have been constructed [ref] .

Masslessness in $n$-dimensions · Discrete UIR of the conformal group · 1.00
These problems have been surveyed in different methods by several authors [ref] .

Black Holes, Information, and Hilbert Space for Quantum Gravity · Introduction · 0.96

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.