相关论文: Spinfoam on Lefschetz Thimble: Markov Chain Monte-…
We study the semiclassical behavior of Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam model, by taking into account the sum over spins in the large spin regime. We also employ the method of stationary phase analysis with parameters…
A new path integral representation of Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam model is derived by employing the theory of unitary representation of SL(2,$\mathbb{C}$). The path integral representation is taken as a starting…
We study the semiclassical behavior of Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam model, by taking into account of the sum over spins in the large spin regime. The large spin parameter \lambda and small Barbero-Immirzi…
Numerical methods are a powerful tool for doing calculations in spinfoam theory. We review the major frameworks available, their definition, and various applications. We start from $\texttt{sl2cfoam-next}$, the state-of-the-art library to…
We numerically study the next-to-leading order corrections of the Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) 4-simplex amplitude in the large-$j$ expansions. We perform large-$j$ expansions of Lorentzian EPRL 4-simplex amplitudes with…
The complex critical points are analyzed in the 4-dimensional Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam model in the large-$j$ regime. For the 4-simplex amplitude, taking into account the complex critical point generalizes the…
We numerically estimate the divergence of several two-vertex diagrams that contribute to the radiative corrections for the Lorentzian EPRL spin foam propagator. We compute the amplitudes as functions of a homogeneous cutoff over the bulk…
The Lorentzian Engle-Pereira-Rovelli-Livine/Freidel-Krasnov (EPRL/FK) spinfoam model and the Conrady-Hnybida (CH) timelike-surface extension can be expressed in the integral form $\int e^S$. This work studies the analytic continuation of…
We study the behaviour of the Lorentzian Engle-Pereira-Rovelli-Livine spinfoam amplitude with homogeneous boundary data, under a graph refinement going from five to twenty boundary tetrahedra. This can be interpreted as a wave function of…
The two-point correlation function is calculated in the Lorentzian EPRL spinfoam model, and shown to match with the one in Regge calculus in a proper limit: large boundary spins, and small Barbero-Immirzi parameter, keeping the size of the…
The intricated combinatorial structure and the non-compactness of the Lorentz group have always made the computation of $SL(2,\mathbb{C})$ EPRL spin foam transition amplitudes a very hard and resource demanding task. With \texttt{sl2cfoam}…
The Lorentzian EPRL spin foam amplitude for loop quantum gravity is a multi-dimensional non-compact integral of highly oscillating functions. Using a method based on the decomposition of Clebsch-Gordan coefficients for the unitary…
We compute transition amplitudes between two spin networks with dipole graphs, using the Lorentzian EPRL model with up to two (non-simplicial) vertices. We find power-law decreasing amplitudes in the large spin limit, decreasing faster as…
Spinfoam amplitudes with small spins can have interesting semiclassical behavior and relate to semiclassical gravity and geometry in 4 dimensions. We study the generalized spinfoam model (Spinfoams for all loop quantum gravity (LQG)) with…
Monte Carlo simulations are useful tools for modeling quantum systems, but in some cases they suffer from a sign problem, leading to an exponential slow down in their convergence to a value. While solving the sign problem is generically…
We provide an algorithm to estimate the divergence degree of the Lorentzian EPRL-FK spin foam amplitudes for arbitrary 2-complexes. We focus on the "self-energy" and "vertex renormalization" diagrams and find an upper bound estimate. We…
The present paper studies the large-j asymptotics of the Lorentzian EPRL spinfoam amplitude on a 4d simplicial complex with an arbitrary number of simplices. The asymptotics of the spinfoam amplitude is determined by the critical…
We introduce a strategy to compute EPRL spin foam amplitudes with many internal faces numerically. We work with sl2cfoam-next, the state-of-the-art framework to numerically evaluate spin foam transition amplitudes. We find that uniform…
We present the benchmark of the polynomial expansion Monte Carlo method to a Kondo lattice model with classical localized spins on a geometrically frustrated lattice. The method enables to reduce the calculation amount by using the…
We develop a numerical method to investigate the semiclassical limit of spin foam amplitudes with many vertices. We test it using the Ponzano-Regge model, a spin foam model for three-dimensional euclidean gravity, and a transition amplitude…