The Classical Limit of the Magnus Expansion

par Pablo Vives Matasan (Queen Mary University of London)

mercredi 18 nov. 2026, 14:45 → 16:00 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Séminaire Amplitudes et Gravitation sur l'Yvette (IHES/IPhT)

The Magnus expansion is a reorganisation of perturbative QFT, computing the operator log of the S-matrix directly. In this talk we will study the classical limit of tree-level Magnus Compton amplitudes with arbitrarily many massless legs. After reviewing the Magnus expansion and its diagrammatic rules, we will focus on a scalar toy model consisting of a massive scalar interacting with a massless one. By working in Schwinger parameter space, we will reframe the classical expansion as a series of identities involving the first Eulerian projector in the algebra of permutations. Within this framework, we show how all hyperclassical terms cancel at the level of the matrix element, and how all classical terms precisely match worldline quantum field theory. Along the way, we uncover a new formula for Murua coefficients and a new identity they satisfy, valid for any tree or acyclic loop graph. Time permitting, I will comment on some intriguing connections to existing literature on the exponentiation of multiple Wilson lines.

 

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