Numerical computations of next-to-leading order corrections in spinfoam large-
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 asymptotics

Han, Muxin; Huang, Zichang; Liu, Hongguang; Qu, Dongxue

doi:10.1103/physrevd.102.124010

Cited by 16 publications

(16 citation statements)

References 26 publications

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“…As such, the action S is a function depending on 54 real parameters. In this parametrization, the measure of the spinor dz becomes dz = dxdy, and the Haar measure dg of SL(2, C) is expressed as (see Appendix A in [51])…”

Section: A Boundary Statementioning

confidence: 99%

“…Taking the coarsest triangulation, R is a 4-simplex, and ∂R is triangulated by five tetrahedra. Specifically, in this paper, we use the boundary geometry introduced in [26,51]. Namely, we set the five vertices of the 4-simplex as 5/3 1/4 ),…”

Section: A Boundary Statementioning

confidence: 99%

“…When we set ζ ab 0 = γΘ ab + 2θ ab , we have ∂ j ab Stot = 0 at one solution and ∂ j ab Stot = 2γΘ ab ∈ 4πZ at the other solution. 8 More details are found [26,51] with Based on the critical g 0ab and z 0ab , we apply our parameterizations ( 11) and ( 12) but let them centered at the critical point:…”

Section: E Critical Pointmentioning

confidence: 99%

See 2 more Smart Citations

Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator

Han,

Huang,

Liu

et al. 2020

Preprint

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We compute numerically the Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam propagator on a 4-simplex, by adapting the methods of Lefschetz thimble and Markov Chain Monte-Carlo to oscillatory spinfoam integrals. Our method can compute any spinfoam observables at relatively large spins. We obtain the numerical results of the propagators at different spins and demonstrate their consistency with the expected spinfoam semi-classical behavior in the large spin limit. Our results exhibit significant quantum corrections at smaller spins. Our method is reliable and thus can be employed to discover the semi-classical and quantum behaviors of the spinfoam model.

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Section: A Boundary Statementioning

confidence: 99%

Section: A Boundary Statementioning

confidence: 99%

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Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator

Han,

Huang,

Liu

et al. 2020

Preprint

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“…However, there has been less progress on quantum corrections in the full theory of LQG dynamics (see e.g. [13,14] for some results in the covariant approach). It is important that as a candidate of quantum gravity theory, LQG should provide predictions on quantum corrections to the classical theory of gravity.…”

Section: Introductionmentioning

confidence: 99%

First-Order Quantum Correction in Coherent State Expectation Value of Loop-Quantum-Gravity Hamiltonian: Overview and Results

Zhang¹,

Song²,

Han³

2020

Preprint

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Given the Loop-Quantum-Gravity (LQG) non-graph-changing Hamiltonian H[N ], the coherent state expectation value H[N ] admits an semiclassical expansion in 2 p . In this paper, we compute explicitly the expansion of H[N ] on the cubic graph to the linear order in 2 p , when the coherent state is peaked at the homogeneous and isotropic data of cosmology. In our computation, a powerful algorithm is developed to overcome the complexity in computing H[N ] . In particular, some key innovations in our algorithm substantially reduce the computational complexity in the Lorentzian part of H[N ] . In addition, some effects in cosmology from the quantum correction in H[N ] are discussed at the end of this paper.

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“…However, regarding the full theory of LQG dynamics, less progress has been made on its quantum corrections (see e.g. [29][30][31][32] for some results, and [33,34] for some results in the covariant approach). As a candidate of quantum gravity theory, it is important that LQG should shed light on quantum corrections to the classical theory of gravity.…”

mentioning

confidence: 99%

First-Order Quantum Correction in Coherent State Expectation Value of Loop-Quantum-Gravity Hamiltonian

Zhang,

Song,

Han

2021

Preprint

Self Cite

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Given the non-graph-changing Hamiltonian H[N ] in Loop Quantum Gravity (LQG), H[N ] , the coherent state expectation value of H[N ], admits an semiclassical expansion in 2 p . In this paper, as presenting the detailed derivations of our previous work [1], we explicitly compute the expansion of H[N ] to the linear order in 2 p on the cubic graph with respect to the coherent state peaked at the homogeneous and isotropic data of cosmology. In our computation, a powerful algorithm is developed, supported by rigorous proofs and several theorems, to overcome the complexity in the computation of H[N ] . Particularly, some key innovations in our algorithm substantially reduce the complexity in computing the Lorentzian part of H[N ] . Additionally, some quantum correction effects resulted from H[N ] in cosmology are discussed at the end of this paper.

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Numerical computations of next-to-leading order corrections in spinfoam large- j asymptotics

Cited by 16 publications

References 26 publications

Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator

Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator

First-Order Quantum Correction in Coherent State Expectation Value of Loop-Quantum-Gravity Hamiltonian: Overview and Results

First-Order Quantum Correction in Coherent State Expectation Value of Loop-Quantum-Gravity Hamiltonian

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