Statistical equilibrium of tetrahedra from maximum entropy principle

Abstract

Discrete formulations of (quantum) gravity in four spacetime dimensions build space out of tetrahedra. We investigate a statistical mechanical system of tetrahedra from a many-body point of view based on non-local, combinatorial gluing constraints that are modelled as multi-particle interactions. We focus on Gibbs equilibrium states, constructed using Jaynes' principle of constrained maximisation of entropy, which has been shown recently to play an important role in characterising equilibrium in background independent systems. We apply this principle first to classical systems of many tetrahedra using different examples of geometrically motivated constraints. Then for a system of quantum tetrahedra, we show that the quantum statistical partition function of a Gibbs state with respect to some constraint operator can be reinterpreted as a partition function for a quantum field theory of tetrahedra, taking the form of a group field theory.

arXiv commentv3 published version; v2 18 pages, 4 figures, improved text in sections IIIC & IVB, minor changes elsewhere

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• Editorial for the Special Issue "Progress in Group Field Theory and Related Quantum Gravity Formalisms"
• Geometrogenesis in GFT: An Analysis
• Curvature from multipartite entanglement in quantum gravity states
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• Cosmological implications of the hydrodynamical phase of group field theory
• Thermofield Double States in Group Field Theory