Finiteness of quantum gravity with matter on a PL spacetime
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913630221500416 |
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| author | Mikovic, Aleksandar |
| author_facet | Mikovic, Aleksandar |
| contents | We study the convergence of the path integral for General Relativity with matter on a picewise linear (PL) spacetime that corresponds to a triangulation of a smooth manifold by using a path-integral measure that renders the pure gravity path integral finite. This measure depends on a parameter p, and in the case when the matter content is just scalar fields, we show that the path integral is absolutely convergent for p > 0,5 and not more than 2 scalar fields. In the case of Yang-Mills fields, we show that the path integral is absolutely convergent for the U(1) group and p > 0,5. In the case of Dirac fermions, we show that the path integral is absolutely convergent for any number of fermions and a sufficiently large p. When the matter content is given by scalars, Yang-Mills fields and fermions, as in the case of the Standard Model, we show that the path integral is absolutely convergent for p > 46,5. Hence one can construct a finite quantum gravity theory on a PL spacetime such that the classical limit is General Relativity coupled to the Standard Model. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_15484 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Finiteness of quantum gravity with matter on a PL spacetime Mikovic, Aleksandar General Relativity and Quantum Cosmology High Energy Physics - Theory We study the convergence of the path integral for General Relativity with matter on a picewise linear (PL) spacetime that corresponds to a triangulation of a smooth manifold by using a path-integral measure that renders the pure gravity path integral finite. This measure depends on a parameter p, and in the case when the matter content is just scalar fields, we show that the path integral is absolutely convergent for p > 0,5 and not more than 2 scalar fields. In the case of Yang-Mills fields, we show that the path integral is absolutely convergent for the U(1) group and p > 0,5. In the case of Dirac fermions, we show that the path integral is absolutely convergent for any number of fermions and a sufficiently large p. When the matter content is given by scalars, Yang-Mills fields and fermions, as in the case of the Standard Model, we show that the path integral is absolutely convergent for p > 46,5. Hence one can construct a finite quantum gravity theory on a PL spacetime such that the classical limit is General Relativity coupled to the Standard Model. |
| title | Finiteness of quantum gravity with matter on a PL spacetime |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2306.15484 |