Summing bulk quantum numbers with Monte Carlo in spin foam theories
Pietro Donà, Pietropaolo Frisoni
Abstract
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 sampling Monte Carlo is exceptionally effective in approximating the sum over internal quantum numbers of a spin foam amplitude, considerably reducing the computational resources necessary. We apply it to compute large volume divergences of the theory and find surprising numerical evidence that the EPRL vertex renormalization amplitude is instead finite.
Topics & Concepts
AmplitudeMonte Carlo methodQuantum Monte CarloPhysicsRenormalizationSpin (aerodynamics)Statistical physicsVertex (graph theory)Spin foamQuantumQuantum mechanicsMathematicsQuantum gravityStatisticsGraphThermodynamicsLoop quantum gravityDiscrete mathematicsQuantum many-body systemsNoncommutative and Quantum Gravity TheoriesAdvanced NMR Techniques and Applications