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Spinfoams and high performance computing
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abstract
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 efficiently compute EPRL spin foam amplitudes based on the booster decomposition. We also review two alternative approaches based on the integration representation of the spinfoam amplitude: Firstly, the numerical computations of the complex critical points discover the curved geometries from the spinfoam amplitude and provides important evidence of resolving the flatness problem in the spinfoam theory. Lastly, we review the numerical estimation of observable expectation values based on the Lefschetz thimble and Markov-Chain Monte Carlo method, with the EPRL spinfoam propagator as an example.
Forward citations
Cited by 3 Pith papers
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Deferred Cyclotomic Representation for Stable and Exact Evaluation of q-Hypergeometric Series
The deferred cyclotomic representation (DCR) is a parameter-independent combinatorial object for q-hypergeometric series that resolves numerator-denominator cancellations exactly as integer arithmetic prior to evaluat...
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Deep learning spinfoam vertex amplitudes: the Euclidean Barrett-Crane model
A proof-of-principle that simple neural networks can learn Euclidean Barrett-Crane 10j vertex amplitudes: classification generalizes to higher cutoffs, regression works only within the trained low-spin domain.
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Les Houches lectures on Spinfoam Path Integrals
A pedagogical review of spinfoam path integrals, from 1d quantum mechanics and 2d BF theory through Ponzano-Regge/Turaev-Viro to the 4d EPRL model, accurate but with no new results.
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