A finiteness bound for the EPRL/FK spin foam model

Abstract

We show that the EPRL/FK spin foam model of quantum gravity has an absolutely convergent partition function if the vertex amplitude is divided by an appropriate power $p$ of the product of dimensions of the vertex spins. This power is independent of the spin foam 2-complex and we find that $p>2$ insures the convergence of the state sum. Determining the convergence of the state sum for the values $0\le p\le 2$ requires the knowledge of the large-spin asymptotics of the vertex amplitude in the cases when some of the vertex spins are large and other are small.

v6: published version

References in corpus (7)

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• Lorentzian spin foam amplitudes: graphical calculus and asymptotics
• Face amplitude of spinfoam quantum gravity
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Cited by in corpus (9)

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• Coupled intertwiner dynamics: A toy model for coupling matter to spin foam models
• Topological invariant of 4-manifolds based on a 3-group
• Gauge symmetry of the 3BF theory for a generic Lie 3-group
• Henneaux-Teitelboim gauge symmetry and its applications to higher gauge theories
• Finiteness of quantum gravity with matter on a PL spacetime
• Transition probability spaces in loop quantum gravity
• Categorical generalization of spinfoam models