Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator
General Relativity and Quantum Cosmology
2021-04-19 v2 High Energy Physics - Lattice
High Energy Physics - Theory
Mathematical Physics
math.MP
Computational Physics
Abstract
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.
Keywords
Cite
@article{arxiv.2012.11515,
title = {Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator},
author = {Muxin Han and Zichang Huang and Hongguang Liu and Dongxue Qu and Yidun Wan},
journal= {arXiv preprint arXiv:2012.11515},
year = {2021}
}
Comments
26 pages, 8 figures, 11 tables