Toller matrices T^(±) in causal spinfoam amplitudes satisfy T^(+) + T^(-) = D and admit equivalent definitions via analyticity, iε prescription, and boost-eigenvalue integrals that reproduce the Euclidean-to-Lorentzian Wick rotation.
Numerical methods for EPRL spin foam transition amplitudes and Lorentzian recoupling theory
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abstract
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} we provide a C-coded library for the evaluation of the Lorentzian EPRL vertex amplitude. We provide a tool to compute the Lorentzian EPRL 4-simplex vertex amplitude in the intertwiner basis and some utilities to evaluate SU(2) invariants, booster functions and $SL(2,\mathbb{C})$ Clebsch-Gordan coefficients. We discuss the data storage, parallelizations, time, and memory performances and possible future developments.
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The emergence of the cosmological arrow of time is identified with a confinement-deconfinement transition in a Z2 lattice gauge theory on LQG spin networks, with the deconfined phase corresponding to a CZX-type SPT phase.
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Toller matrices and the Feynman $i\varepsilon$ in spinfoams
Toller matrices T^(±) in causal spinfoam amplitudes satisfy T^(+) + T^(-) = D and admit equivalent definitions via analyticity, iε prescription, and boost-eigenvalue integrals that reproduce the Euclidean-to-Lorentzian Wick rotation.
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Gauging Time Reversal Symmetry in Quantum Gravity: Arrow of Time from a Confinement--Deconfinement Transition
The emergence of the cosmological arrow of time is identified with a confinement-deconfinement transition in a Z2 lattice gauge theory on LQG spin networks, with the deconfined phase corresponding to a CZX-type SPT phase.