Spinfoam Models for Quantum Gravity: Overview
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912178883264512 |
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| author | Livine, Etera R. |
| author_facet | Livine, Etera R. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09364 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spinfoam Models for Quantum Gravity: Overview Livine, Etera R. General Relativity and Quantum Cosmology 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. |
| title | Spinfoam Models for Quantum Gravity: Overview |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2403.09364 |