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Letters in Mathematical Physics

, Volume 105, Issue 6, pp 795–825 | Cite as

A Schwinger–Dyson Equation in the Borel Plane: Singularities of the Solution

  • Marc P. Bellon
  • Pierre J. Clavier
Article

Abstract

We map the Schwinger–Dyson equation and the renormalization group equation for the massless Wess–Zumino model in the Borel plane, where the product of functions gets mapped to a convolution product. The two-point function can be expressed as a superposition of general powers of the external momentum. The singularities of the anomalous dimension are shown to lie on the real line in the Borel plane and to be linked to the singularities of the Mellin transform of the one-loop graph. This new approach allows us to enlarge the reach of previous studies on the expansions around those singularities. The asymptotic behavior at infinity of the Borel transform of the solution is beyond the reach of analytical methods and we do a preliminary numerical study, aiming to show that it should remain bounded.

Keywords

renormalization Schwinger–Dyson equation Borel transform alien calculus 

Mathematics Subject Classification

81Q40 81T16 40G10 

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Sorbonne Universités, UPMC Univ Paris 06, UMR 7589, LPTHEParisFrance
  2. 2.CNRS, UMR 7589, LPTHEParisFrance

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