Holonomy-flux spinfoam amplitude

Abstract

We introduce a holomorphic representation for the Lorentzian EPRL spinfoam on arbitrary 2-complexes. The representation is obtained via the Ashtekar-Lewandowski-Marolf-Mourão-Thiemann heat kernel coherent state transform. The new variables are classical holonomy-flux phase space variables $(h,X)\simeq {\mathcal{T}}^{\ast }SU(2)$ of Hamiltonian loop quantum gravity prescribing the holonomies of the Ashtekar connection $A=\Gamma +\gamma K$, and their conjugate gravitational fluxes. For small heat kernel `time' the spinfoam amplitude is peaked on classical space-time geometries, where at most countably many curvatures are allowed for non-zero Barbero-Immirzi parameter. We briefly comment on the possibility to use the alternative flipped classical limit.

33 pages

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Cited by in corpus (8)

• Regge gravity from spinfoams
• Semiclassical Limit of New Path Integral Formulation from Reduced Phase Space Loop Quantum Gravity
• Addendum: EPRL/FK Asymptotics and the Flatness Problem
• On Spinfoams Near a Classical Curvature Singularity
• The accidental flatness constraint does not mean a wrong classical limit
• Spinfoams: Foundations
• Semi-Classical Holomorphic Transition Amplitudes in Covariant Loop Quantum Gravity
• Geometry Transition in Covariant Loop Quantum Gravity