The Analytic Evolution of Dyson–Schwinger Equations via Homomorphism Densities
| Autor: | Ali Shojaei-Fard |
|---|---|
| Přispěvatelé: | Institut des Hautes Etudes Scientifiques (IHES), IHES |
| Rok vydání: | 2021 |
| Předmět: |
Feynman graph
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] Gâteaux derivative Banach space Space (mathematics) 01 natural sciences Separable space symbols.namesake 0103 physical sciences Taylor series Feynman diagram Gauge theory 0101 mathematics Mathematical Physics Mathematical physics Physics Coupling constant algebra: Hopf Taylor expansion Homomorphism densities of graphons 010102 general mathematics field theory: nonperturbative coupling constant Dyson-Schwinger equation symbols gauge field theory Homomorphism Feynman graphons 010307 mathematical physics Geometry and Topology Combinatorial Dyson–Schwinger equations Non-perturbative QFT |
| Zdroj: | Math.Phys.Anal.Geom. Math.Phys.Anal.Geom., 2021, 24 (2), pp.18. ⟨10.1007/s11040-021-09389-z⟩ |
| ISSN: | 1572-9656 1385-0172 |
| DOI: | 10.1007/s11040-021-09389-z |
| Popis: | Feynman graphon representations of Feynman diagrams lead us to build a new separable Banach space $\mathcal {S}^{\Phi ,g}_{\approx }$ originated from the collection of all Dyson–Schwinger equations in a given (strongly coupled) gauge field theory Φ with the bare coupling constant g. We study the Gâteaux differential calculus on the space of functionals on $\mathcal {S}^{\Phi ,g}_{\approx }$ in terms of a new class of homomorphism densities. We then show that Taylor series representations of smooth functionals on $\mathcal {S}^{\Phi ,g}_{\approx }$ provide a new analytic description for solutions of combinatorial Dyson–Schwinger equations. |
| Databáze: | OpenAIRE |
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