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  • Open Access

Nonperturbative S-Matrix Renormalization

Laurent Freidel1,*, José Padua-Argüelles1,2,†, Susanne Schander1,‡, and Marc Schiffer3,§

  • 1Perimeter Institute, 31 Caroline Street North, Waterloo, Ontario, N2L 2Y5, Canada
  • 2Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1, Canada
  • 3High Energy Physics Department, Institute for Mathematics, Astrophysics, and Particle Physics, Radboud University, Nijmegen, The Netherlands

  • *Contact author: lfreidel@pitp.ca
  • †Contact author: jpaduaarguelles@pitp.ca
  • ‡Contact author: sschander@pitp.ca
  • §Contact author: marc.schiffer@ru.nl
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Phys. Rev. Lett. 136, 251602 – Published 24 June, 2026

DOI: https://doi.org/10.1103/jxcl-q2vt

Abstract

We propose a renormalization group flow equation for a functional that generates S-matrix elements and which captures similarities to the well-known Wetterich and Polchinski equations. While the latter ones, respectively, involve the effective action and Schwinger functional, which are genuine off-shell objects, the presented flow equation has the advantage of working more directly with observables, i.e., scattering amplitudes. Compared to the Wetterich equation, our flow equation also greatly simplifies the notion of going on shell, in the sense of satisfying the quantum equations of motion. In addition, unlike the Wetterich equation, it is polynomial and does not require a Hessian inversion. The approach is a promising direction for nonperturbative quantum field theories, allowing one to work more directly with scattering amplitudes.

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References (44)

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Phys. Rev. Lett. 136, 251602– Published 24 June, 2026
  • Received 3 March 2026
  • Revised 19 May 2026
  • Accepted 29 May 2026
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