On the interplay between boundary conditions and the Lorentzian Wetterich equation
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913196182339584 |
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| author | Dappiaggi, Claudio Nava, Filippo Sinibaldi, Luca |
| author_facet | Dappiaggi, Claudio Nava, Filippo Sinibaldi, Luca |
| contents | In the framework of the functional renormalization group and of the perturbative, algebraic approach to quantum field theory (pAQFT), in [DDPR23] it has been derived a Lorentian version of a flow equation à la Wetterich, which can be used to study non linear, quantum scalar field theories on a globally hyperbolic spacetime. In this work we show that the realm of validity of this result can be extended to study interacting scalar field theories on globally hyperbolic manifolds with a timelike boundary. By considering the specific examples of half Minkowski spacetime and of the Poincaré patch of Anti-de Sitter, we show that the form of the Lorentzian Wetterich equation is strongly dependent on the boundary conditions assigned to the underlying field theory. In addition, using a numerical approach, we are able to provide strong evidences that there is a qualitative and not only a quantitative difference in the associated flow and we highlight this feature by considering Dirichlet and Neumann boundary conditions on half Minkowski spacetime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07130 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the interplay between boundary conditions and the Lorentzian Wetterich equation Dappiaggi, Claudio Nava, Filippo Sinibaldi, Luca Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory In the framework of the functional renormalization group and of the perturbative, algebraic approach to quantum field theory (pAQFT), in [DDPR23] it has been derived a Lorentian version of a flow equation à la Wetterich, which can be used to study non linear, quantum scalar field theories on a globally hyperbolic spacetime. In this work we show that the realm of validity of this result can be extended to study interacting scalar field theories on globally hyperbolic manifolds with a timelike boundary. By considering the specific examples of half Minkowski spacetime and of the Poincaré patch of Anti-de Sitter, we show that the form of the Lorentzian Wetterich equation is strongly dependent on the boundary conditions assigned to the underlying field theory. In addition, using a numerical approach, we are able to provide strong evidences that there is a qualitative and not only a quantitative difference in the associated flow and we highlight this feature by considering Dirichlet and Neumann boundary conditions on half Minkowski spacetime. |
| title | On the interplay between boundary conditions and the Lorentzian Wetterich equation |
| topic | Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2401.07130 |