New scalar constraint operator for loop quantum gravity

Assanioussi, Mehdi; Lewandowski, Jerzy; Mäkinen, Ilkka

doi:10.1103/physrevd.92.044042

Cited by 57 publications

(95 citation statements)

References 21 publications

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“…There is a different proposal for the Hamiltonian operator by Alesci-Assanioussi-Lewandowski-Makinen (AALM) [40,41], based on a classically equivalent expression of the Hamiltonian constraint:…”

Section: Alesci-assanioussi-lewandowski-makinen's Hamiltonianmentioning

confidence: 99%

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Effective dynamics from coherent state path integral of full loop quantum gravity

Han

Liu

2020

Phys. Rev. D

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A new routine is proposed to relate Loop Quant Cosmology (LQC) to Loop Quantum Gravity (LQG) from the perspective of effective dynamics. We derive the big-bang singularity resolution and big bounce from the first principle of full canonical LQG. Our results are obtained in the framework of the reduced phase space quantization of LQG. As a key step in our work, we derive with coherent states a new discrete path integral formula of the transition amplitude generated by the physical Hamiltonian. The semiclassical approximation of the path integral formula gives an interesting set of effective equations of motion (EOMs) for full LQG. When solving the EOMs with homogeneous and isotropic ansatz, we reproduce the LQC effective dynamics in µ 0 -scheme. The solution replaces the big-bang singularity by a big bounce. In the end, we comment on the possible relation between theμ-scheme of effective dynamics and the continuum limit of the path integral formula. arXiv:1910.03763v2 [gr-qc] 23 Dec 20191 The result is also valid in the case of an infinite space. 2 E(γ) and V(γ) denote the set of edges and vertices in γ.

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Section: Alesci-assanioussi-lewandowski-makinen's Hamiltonianmentioning

confidence: 99%

“…There are two popular Hamiltonians of LQG, based on Giesel-Thiemann's construction [32,38], and the construction by Alesci-Assanioussi-Lewandowski-Makinen (AALM) [39,40] using scalar curvature operator [41]. Our work analyzes both possibilities.…”

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confidence: 99%

Effective dynamics from coherent state path integral of full loop quantum gravity

Han

Liu

2020

Phys. Rev. D

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“…Recently, considerable attention has been paid to studying the mathematical ambiguities that affect the formulation of LQC and, in particular, to explore alternatives to the standard regularization of the Hamiltonian constraint [22][23][24]. One of these alternatives has reached a more prominent status, because it is especially interesting from the physical point of view.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Dapor-Liegener formalism of loop quantum cosmology for Bianchi I spacetimes

García-Quismondo

Marugán

2020

Phys. Rev. D

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We discuss the quantization of vacuum Bianchi I spacetimes in the modified formalism of loop quantum cosmology recently proposed by Dapor and Liegener. This modification is based on a regularization procedure where both the Euclidean and Lorentzian terms of the Hamiltonian are treated independently. Whereas the Euclidean part has already been dealt with in the literature for Bianchi I spacetimes, the Lorentzian one has not yet been represented quantum mechanically. After a brief review of the quantum kinematics and the quantization of the Euclidean sector, we represent the Lorentzian part of the Hamiltonian constraint by an operator according to the factor ordering rules of the Martín-Benito-Mena Marugán-Olmedo prescription. We study the general properties of this quantum operator and the superselection rules derived therefrom, resulting in an action similar to that of the Euclidean operator except that the orientation of the densitized triad is not preserved, a fact which leads to a generic enlargement of the superselection sectors. We conclude with an explanation of the mechanism that prevents this enlargement in the isotropic case and a comment on the effect of alternative prescriptions for the implementation of the improved dynamics.

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“…It should be noted that although the symmetry adapted variables only depend on x, y their indices run from 1 to 3. The total Hamiltonian in terms of the reduced variables is, 4) and the (smeared) constraints are, g( λ) = 1 β dxdyλ i ∂ a e a i + ε ijk a j a e a k + ε ijk δ j 3 δ φ a e a k , (2.5) h L (N ) = 2 dxdy N √ e (1 + β 2 ) ijk ilm e a j e b k k l a k m b , (2.8) where we have written the scalar constraint as c(N ) = h E (N ) + h L (N ).…”

Section: Summary Of the Classical Theorymentioning

confidence: 99%