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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.17922 |
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| _version_ | 1866911732378632192 |
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| author | Losev, Andrey Sheptunov, Dmitrii Geng, Xin |
| author_facet | Losev, Andrey Sheptunov, Dmitrii Geng, Xin |
| contents | One of the approaches to quantum gravity is to formulate it in terms of De Rham algebra, choose a triangulation of space-time, and replace differential forms by cochains (that form a finite dimensional vector space). The key issue of general relativity is the action of diffeomorphisms of space-time on fields.
In this paper, we induce the action of diffeomorphisms on cochains by homotopy transfer (or, equivalently, BV integral) that leads to a $L_{\infty}$ action.
We explicitly compute this action for the space-time being an interval, a circle, and a square. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17922 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On induced L-infinity action of diffeomorphisms on Cochains Losev, Andrey Sheptunov, Dmitrii Geng, Xin Mathematical Physics One of the approaches to quantum gravity is to formulate it in terms of De Rham algebra, choose a triangulation of space-time, and replace differential forms by cochains (that form a finite dimensional vector space). The key issue of general relativity is the action of diffeomorphisms of space-time on fields. In this paper, we induce the action of diffeomorphisms on cochains by homotopy transfer (or, equivalently, BV integral) that leads to a $L_{\infty}$ action. We explicitly compute this action for the space-time being an interval, a circle, and a square. |
| title | On induced L-infinity action of diffeomorphisms on Cochains |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2406.17922 |