RECORD
Coherent State Functional Integrals in Quantum Cosmology
General Relativity and Quantum Cosmology · Submitted 25 Oct 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This reveals the intrinsic relation among coherent state functional integral, effective theory and star-product.
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
The abstract, sentence by sentence
Coherent state functional integrals for the minisuperspace models of quantum cosmology are studied. By the well-established canonical theories, the transition amplitudes in the path-integral representations of Wheeler-DeWitt quantum cosmology and loop quantum cosmology can be formulated through group averaging. The effective action and Hamiltonian with higher-order quantum corrections are thus obtained in both models. It turns out that for a non-symmetric Hamiltonian constraint operator, the Moyal (star)-product emerges naturally in the effective Hamiltonian. This reveals the intrinsic relation among coherent state functional integral, effective theory and star-product. Moreover, both the resulted effective theories imply a possible quantum cosmological effect in large scale limit.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Coherent state functional integrals for the minisuperspace models of quantum cosmology are studied. | contribution 0.94 | 0.82 | 0.04 | asserted 0.92 |
| s1 | By the well-established canonical theories, the transition amplitudes in the path-integral representations of Wheeler-DeWitt quantum cosmology and loop quantum cosmology can be formulated through group averaging. | method 0.61 | 0.13 | 0.06 | asserted 0.97 |
| s2 | The effective action and Hamiltonian with higher-order quantum corrections are thus obtained in both models. | result 0.97 | 0.85 | 0.13 | asserted 1.00 |
| s3 | It turns out that for a non-symmetric Hamiltonian constraint operator, the Moyal (star)-product emerges naturally in the effective Hamiltonian. | result 1.00 | 0.85 | 0.26 | asserted 1.00 |
| s4 | This reveals the intrinsic relation among coherent state functional integral, effective theory and star-product. | interpretation 0.99 | 0.81 | 0.57 | asserted 1.00 |
| s5 | Moreover, both the resulted effective theories imply a possible quantum cosmological effect in large scale limit. | interpretation 0.89 | 0.82 | 0.34 | hedged possibility 1.00 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
Coherent state functional integrals for the minisuperspace models of quantum cosmology are studied. By the well-established canonical theories, the transition amplitudes in the path-integral representations of Wheeler-DeWitt quantum cosmology and loop quantum cosmology can be formulated through group averaging. The effective action and Hamiltonian with higher-order quantum corrections are thus obtained in both models. It turns out that for a non-symmetric Hamiltonian constraint operator, the Moyal (star)-product emerges naturally in the effective Hamiltonian. This reveals the intrinsic relation among coherent state functional integral, effective theory and star-product. Moreover, both the resulted effective theories imply a possible quantum cosmological effect in large scale limit.
Human review
How the literature uses it
9 arXiv papers cite this in 12 sentences
Papers citing it · 5 sentences without a confident label
Uses its method or tool 1 paper
-
The product of the matrix elements in eqn:A matter can be calculated as [ref] : ∏_n=1^Nne^i_np̂_ϕ^2/ħ^2n-1/nn-1 =(∏_n=1^N nn-1/nn-1) exp[i_n/ħ^2 ∑_n=1^N(p_ϕ_n-1^2+ħ^2/_̧n^2+_̧n-1^2)], where the product of series$nn-1$can be expressed as ∏_n=1^N nn-1/nn-1 =exp[ϕ_N^2+p_ϕ_N^2_̧N+1^2_̧N^2/ħ^2/2(_̧N+1^2+_̧N^2) -ϕ_0^2+p_ϕ_0^2_̧1^2_̧0^2/ħ^2/2(_̧1^2+_̧0^2)] (∏_n=1^N√(2_̧n_̧n-1/_̧n^2+_̧n-1^2)) ·exp[∑_n=1^N(-2(_̧n+1^2+_̧n^2)ϕ_nϕ_n-ϕ_n-1/ -(_̧n+1+_̧n-1)_̧n+1-_̧n-1/ϕ_n^2/2(_̧n+1^2+_̧n^2)(_̧n^2+_̧n-1^2) +i/ħp_ϕ_n ϕ_n-ϕ_n-1/ -1/4ħ^24(_̧n+1^2_̧n^2_̧n-1^2+_̧n^4_̧n-1^2)p_ϕ_n p_ϕ_n-p_ϕ_n-1/ +2_̧n^4(_̧n+1+_̧n-1)_̧n+1-_̧n-1/p_ϕ_n^2/(_̧n+1^2+_̧n^2)(_̧n^2+_̧n-1^2))].
Coherent State Functional Integral in Loop Quantum Cosmology: Alternative Dynamics · Coherent functional integrals · 0.94
Compares with it 1 paper
-
The resulting effective Hamiltonian in the reference [ [ref] ] is, (considering the difference in denotations) [equation] It contains the fluctuation $ħ^2/2σ^2$ of $p_ϕ$ corresponding to $0020$, the fluctuation $δ^2/2$ of $$̌ corresponding to$2000$and the fluctuation$ħ^2/2δ^2$of$b$which is the same as$0200$.
Effective Theories of Quantum Cosmology · Discussion · 0.97
Cites it as background 3 papers
-
The coherent state functional integrals are also proposed to study quantum cosmological models [ref] .
Path Integrals and Alternative Effective Dynamics in Loop Quantum Cosmology · Introduction · 0.91
-
The effective equations of LQC are being studied from both the canonical perspective [ref] and the path integral perspective [ref] .
Anomaly freedom of the vector modes with holonomy corrections in perturbative Euclidean loop quantum gravity · Introduction · 0.93
-
Even a coherent state functional has been studied for some models [ref] .
Path integral polymer propagator of relativistic and non-relativistic particles · Introduction · 0.92
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.