Speaker
Description
Resurgence in Ward–Schwinger–Dyson Equations for QED
Edwyn Tecedor (1)(3), Marc Bellon (1)(2), Redamy Perez-Ramos (1)(3)
(1) Sorbonne Université LPTHE , CNRS (2), IPSA (3), Paris, France
Perturbative expansions in quantum field theory are divergent, with coefficients exhibiting factorial growth. Resurgence analysis provides a systematic framework to decode this growth and extract non-perturbative information via the Borel–Laplace resummation and alien calculus [1]. The Ward–Schwinger–Dyson (WSD) approach yields exact, regularisation-independent equations for the Green functions, compatible with the renormalisation group, and has been shown to provide a natural setting for resurgent analysis in the φ³₆ model [2, 3].
We extend this programme to massless QED in four dimensions. The presence of two coupled propagator equations, the Ward–Takahashi identity constraining the vertex [4], and the infrared structure of 4D, each introduce new features with respect to the scalar case. We set up the WSD system for the QED vertex using momentum differentiation and infrared rearrangement, reducing the determination of the anomalous dimension to the evaluation of a single-scale loop integral whose Mellin residue encodes the full resurgent structure. The non-trivial Dirac algebra of the theory is handled systematically and contributes a numerator that modifies the pole structure of the Borel transform with respect to φ³₆.
We present the current state of this ongoing work and discuss the open questions that remain on the road to a full resurgent analysis of QED.
[1] J. Ecalle ,Les fonctions résurgentes, Algèbres de fonctions résurgentes. Publ. Math. Orsay 81.05 (1981).
[2] M. P. Bellon, E. I. Russo, Ward–Schwinger–Dyson equations in φ³₆ quantum field theory, Lett. Math. Phys. 111 (2021), arXiv:2007.15675.
[3] M. P. Bellon, E. I. Russo, Resurgent analysis of Ward–Schwinger–Dyson equations, SIGMA 17 (2021), arXiv:2011.13822.
[4] J. C. Ward, Renormalization theory of the interactions of nucleons, mesons and photons, Phys. Rev. 84 (1951).
| Affiliation | LPTHE - Sorbonne Université |
|---|---|
| Career status | PhD student |