A Wick rotation for EPRL spin foam models

Abstract

We show that the Euclidean and Lorentzian EPRL vertex amplitudes of covariant Loop Quantum Gravity are related through a ``Wick rotation'' of the real Immirzi parameter to purely imaginary values. Our result follows from the simultaneous analytic continuation of the algebras, group elements and unitary irreducible representations of the gauge groups $Spin(4)$ and $SL(2,\mathbb{C})$, applied to the decomposition of the two models in terms of $SU(2)$ invariants and booster functions.

25 pages, 1 figure

References in corpus (5)

• LQG vertex with finite Immirzi parameter
• A New Spin Foam Model for 4d Gravity
• Quantum Corrections in the Group Field Theory Formulation of the EPRL/FK Models
• Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator
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Cited by in corpus (3)

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