Statistical equilibrium of tetrahedra from maximum entropy principle

Goffredo Chirco, Isha Kotecha, and Daniele Oriti
Phys. Rev. D 99, 086011 – Published 12 April 2019

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 nonlocal, combinatorial gluing constraints that are modeled as multiparticle interactions. We focus on Gibbs equilibrium states, constructed using Jaynes’s principle of constrained maximization of entropy, which has been shown recently to play an important role in characterizing 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.

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  • Received 28 February 2019

DOI:https://doi.org/10.1103/PhysRevD.99.086011

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & AstrophysicsStatistical Physics & ThermodynamicsQuantum Information, Science & Technology

Authors & Affiliations

Goffredo Chirco1,*, Isha Kotecha1,2,†, and Daniele Oriti1,3,‡

  • 1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam-Golm, Germany
  • 2Institute for Physics, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
  • 3Arnold-Sommerfeld-Center for Theoretical Physics, Ludwig-Maximilians-Universität Theresienstrasse 37, D-80333 München, Germany

  • *goffredo.chirco@aei.mpg.de
  • isha.kotecha@aei.mpg.de
  • daniele.oriti@aei.mpg.de

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Issue

Vol. 99, Iss. 8 — 15 April 2019

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