Existence theorem on the UV limit of Wilsonian RG flows of Feynman measures
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arXiv
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| Format: | Preprint |
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2025
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| author | Laszlo, Andras Tarcsay, Zsigmond Ziebell, Jobst |
| author_facet | Laszlo, Andras Tarcsay, Zsigmond Ziebell, Jobst |
| contents | In nonperturbative formulation of Euclidean signature quantum field theory (QFT), the vacuum state is characterized by the Wilsonian renormalization group (RG) flow of Feynman measures. Such an RG flow is a family of Feynman measures on the space of ultraviolet (UV) regularized fields, linked by the Wilsonian renormalization group equation. In this paper we show that under mild conditions, a Wilsonian RG flow of Feynman measures extending to arbitrary regularization strengths has a factorization property: there exists an ultimate Feynman measure (UV limit) on the distribution sense fields, such that the regularized instances in the flow are obtained from this UV limit via taking the marginal measure against the regulator. Existence theorems on the flow and UV limit of the corresponding action functional are also discussed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_16319 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence theorem on the UV limit of Wilsonian RG flows of Feynman measures Laszlo, Andras Tarcsay, Zsigmond Ziebell, Jobst High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics 81T08 (Primary), 81T16, 81T17, 81T20, 81T27 (Secondary) In nonperturbative formulation of Euclidean signature quantum field theory (QFT), the vacuum state is characterized by the Wilsonian renormalization group (RG) flow of Feynman measures. Such an RG flow is a family of Feynman measures on the space of ultraviolet (UV) regularized fields, linked by the Wilsonian renormalization group equation. In this paper we show that under mild conditions, a Wilsonian RG flow of Feynman measures extending to arbitrary regularization strengths has a factorization property: there exists an ultimate Feynman measure (UV limit) on the distribution sense fields, such that the regularized instances in the flow are obtained from this UV limit via taking the marginal measure against the regulator. Existence theorems on the flow and UV limit of the corresponding action functional are also discussed. |
| title | Existence theorem on the UV limit of Wilsonian RG flows of Feynman measures |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics 81T08 (Primary), 81T16, 81T17, 81T20, 81T27 (Secondary) |
| url | https://arxiv.org/abs/2502.16319 |