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Spinfoam Models for Quantum Gravity: Overview (2403.09364v2)

Published 14 Mar 2024 in gr-qc

Abstract: In the quest of a physical theory of quantum gravity, spin foam models, or in short spinfoams, propose a well-defined path integral summing over quantized discrete space-time geometries. At the crossroad of topological quantum field theory, dynamical triangulations, Regge calculus, and loop quantum gravity, this framework provides a non-perturbative and background independent quantization of general relativity. It defines transition amplitudes between quantum states of geometry, and gives a precise picture of the Planck scale geometry with quantized areas and volumes. Gravity in three space-time dimensions is exactly quantized in terms of the Ponzano-Regge state-sum and Turaev-Viro topological invariants. In four space-time dimensions, gravity is formulated as a topological theory, of the BF type, with extra constraints, and hence quantized as a topological state-sum filled with defects. This leads to the Engle-Pereira-Rovelli-Livine (EPRL) spinfoam model, that can be used for explicit quantum gravity computations, for example for resolving the Big Bang singularity by a bounce or in black-to-white hole transition probability amplitudes.

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  1. Etera R. Livine
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