Curvature operator for loop quantum gravity

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.

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.…”

mentioning

confidence: 99%

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

Han

Liu

2020

“…Some consistency checks [9] [10] [11] on different regularization methods have been done in order to choose suitable construction and fix the regularization ambiguity. It turns out that many geometric quantities, including length [12] [13] [14], area [5] [6], volume [5] [7], angle [15], metric components [16], and spatial Riemann curvature scalar [17], have been quantized as well-defined operators in the kinematic Hilbert space of LQG [6] [18] [19] [20]. The starting point of LQG is the Ashtekar-Barbero connection dynamics of (1+3)-dimensional GR.…”

Section: Introductionmentioning

confidence: 99%

General geometric operators in all dimensional loop quantum gravity

Long

2020

Two strategies for constructing general geometric operators in all dimensional loop quantum gravity are proposed. The different constructions are mainly come from the two different regularization methods for the de-densitized dual momentum, which play the role of building block for the spatial geometry. The first regularization method is a generalization of the regularization of the length operator in standard (1 + 3)-dimensional loop quantum gravity, while the second method is a natural extension of those for standard (D-1)-area and D-volume operators. Two versions of general geometric operators to measure arbitrary m-areas are constructed, and their properties are discussed and compared. They serve as valuable candidates to study the quantum geometry in arbitrary dimensions.

“…Nonetheless, the formulation of LQC is not unambiguous. Indeed, the regularization of the Hamiltonian constraint (which generates time reparametrizations once the spatial diffeomorphisms and the Gauss constraints have been imposed) involves certain ambiguities [22][23][24], which were originally resolved by appealing to some apparently natural physical criteria. However, a new tendency has arisen recently: other options that result in viable physical pictures are being examined by comparing their physical predictions.…”

Section: Introductionmentioning

confidence: 99%

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

García-Quismondo

Marugán

2020

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.