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JOURNALS // Symmetry, Integrability and Geometry: Methods and Applications // Archive

SIGMA, 2021 Volume 17, 075, 18 pp. (Mi sigma1757)

This article is cited in 2 papers

Resurgent Analysis of Ward–Schwinger–Dyson Equations

Marc P. Bellon, Enrico I. Russo

Sorbonne Université, CNRS, Laboratoire de Physique Théorique et Hautes Energies, Paris, France

Abstract: Building on our recent derivation of the Ward–Schwinger–Dyson equations for the cubic interaction model, we present here the first steps of their resurgent analysis. In our derivation of the WSD equations, we made sure that they had the properties of compatibility with the renormalisation group equations and independence from a regularisation procedure which was known to allow for the comparable studies in the Wess–Zumino model. The interactions between the transseries terms for the anomalous dimensions of the field and the vertex is at the origin of unexpected features, for which the effect of higher order corrections is not precisely known at this stage: we are only at the beginning of the journey to use resurgent methods to decipher non-perturbative effects in quantum field theory.

Keywords: renormalization, Schwinger–Dyson equation, resurgence.

MSC: 81Q40, 81T16, 40G10

Received: February 10, 2021; in final form July 30, 2021; Published online August 11, 2021

Language: English

DOI: 10.3842/SIGMA.2021.075



Bibliographic databases:
ArXiv: 2011.13822


© Steklov Math. Inst. of RAS, 2024