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Résumé |
Tropical field theory is a recently developed approximation scheme for Feynman integrals. The original definition was combinatorial, and based on the Schwinger-parametric representation of Feynman integrals, but there is an equivalent perspective based on analytic continuation of long-range field theory. Summing over all diagrams, the tropical amplitudes at zero momentum transfer satisfy a partial differential equation, the tropical loop equation.
Tropical field theory is multiplicatively renormalizable, and contains all the Feynman diagrams of ordinary scalar theories, which makes it an excellent model for renormalization of Feynman integrals including all topologies of vertex subdivergences. The renormalized tropical amplitudes satisfy a partial differential equation that coincides with the local potential approximation of the functional renormalization group, giving yet another physical interpretation: Tropical field theory is the Feynman-diagram expansion of the local potential approximation.
Based on recent joint work with Erik Panzer, https://arxiv.org/abs/2512.21091 |
