Perturbation expansions at large order: results for scalar field theories revisited

DOI10.1088/1751-8121/aaf768zbMath1422.81146arXiv1807.00656OpenAlexW2811316409MaRDI QIDQ5235240

Alan J. McKane

Publication date: 7 October 2019

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.00656

zbMATH Keywords

epsilon-expansionscalar field theoriesasymptotic form of perturbation expansions

Mathematics Subject Classification ID

Model quantum field theories (81T10) Perturbative methods of renormalization applied to problems in quantum field theory (81T15) Feynman diagrams (81T18)

Related Items (8)

Non-perturbative completion of Hopf-algebraic Dyson-Schwinger equations ⋮ Resonant resurgent asymptotics from quantum field theory ⋮ Semiclassical trans-series from the perturbative Hopf-algebraic Dyson-Schwinger equations: \(\phi^3\) QFT in 6 dimensions ⋮ \( \hbox{Next-to}{}^k\) leading log expansions by chord diagrams ⋮ Tropical Monte Carlo quadrature for Feynman integrals ⋮ Resummation in QFT with Meijer G-functions ⋮ The critical \(O(N)\) CFT: methods and conformal data ⋮ Statistics of Feynman amplitudes in \(\phi^4\)-theory

Cites Work

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• Large-order asymptotic terms in perturbation theory: the first \((4-\epsilon )\)-expansion correction to renormalization constants in the \(O(n)\)-symmetric theory
• The \(\Phi_4^3\) and \(\Phi_6^3\) matricial QFT models have reflection positive two-point function
• Renormalized asymptotic enumeration of Feynman diagrams
• Two-loop corrections to large order behavior of \(\phi^{4}\) theory
• Elliptic integral evaluations of Bessel moments and applications
• Euler and the Zeta Function
• Six-loop renormalization group functions ofO(n)-symmetric ϕ⁶-theory and ϵ-expansions of tricritical exponents up to ϵ³
• Theory of Bound States in a Random Potential
• Asymptotic behavior of renormalization constants in higher orders of the perturbation expansion for the \((4-\varepsilon)\)-dimensionally regularized \(O(n)\)-symmetric \(\phi^4\) theory

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