Dyson–Schwinger approach to pion–nucleon scattering using time-ordered perturbation theory

Boris Blankleider, Jordan Wray, Alexander Khvinikidze

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We present a simple description of pion–nucleon (πN) scattering taking into account the full complexity of pion absorption and creation on the nucleon. To do this, we solve Dyson–Schwinger equations within the framework of time-ordered perturbation theory. This enables us to construct partial wave separable πN t matrices that can be useful in models of nuclear processes involving fully dressed nucleons. At the same time, our approach demonstrates features of quantum field theory, such as particle dressing, renormalization, and the use of Dyson–Schwinger equations, in a non-relativistic context that is maximally close to that of quantum mechanics. For this reason, this article may also be of pedagogical interest.
Original languageEnglish
Article number025204
Number of pages11
JournalAIP Advances
Issue number2
Publication statusPublished - 1 Feb 2021


  • Pion-nucleon scattering
  • perturbation theory
  • Dyson-Schwinger equations
  • quantum field theory
  • quantum mechanics


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