Stochastic dynamics for Group Field Theories
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909772838600704 |
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| author | Lahoche, Vincent Samary, Dine Ousmane |
| author_facet | Lahoche, Vincent Samary, Dine Ousmane |
| contents | Phase transitions with spontaneous symmetry breaking are expected for group field theories as a basic feature of the geometogenesis scenario. The following paper aims to investigate the equilibrium phase for group field theory by using the ergodic hypothesis on which the Gibbs-Boltzmann distributions must break down. The breaking of the ergodicity can be considered dynamically, by introducing a fictitious time inducing a stochastic process described through a Langevin equation, from which the randomness of the tensor field will be a consequence. This type of equation is considered particularly for complex just-renormalizable Abelian model of rank d = 5, and we study some of their properties by using a renormalization group considering a coarse-graining both in time and space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_02321 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Stochastic dynamics for Group Field Theories Lahoche, Vincent Samary, Dine Ousmane Mathematical Physics High Energy Physics - Theory Phase transitions with spontaneous symmetry breaking are expected for group field theories as a basic feature of the geometogenesis scenario. The following paper aims to investigate the equilibrium phase for group field theory by using the ergodic hypothesis on which the Gibbs-Boltzmann distributions must break down. The breaking of the ergodicity can be considered dynamically, by introducing a fictitious time inducing a stochastic process described through a Langevin equation, from which the randomness of the tensor field will be a consequence. This type of equation is considered particularly for complex just-renormalizable Abelian model of rank d = 5, and we study some of their properties by using a renormalization group considering a coarse-graining both in time and space. |
| title | Stochastic dynamics for Group Field Theories |
| topic | Mathematical Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2209.02321 |