Topological Recursion and Quantum Path Signatures

2026/08/03 by Inês Aniceto, Thomas Cass, Samuel Crew
Physics and Astronomy · Mathematics · #math-ph #hep-th #math.MP #math.PR #quant-ph

paper · pdf

21 pages, 1 figure

arxiv created 2026/08/03 · arxiv updated 2026/08/05

Abstract

We introduce a non-commutative Laplace transform between functionals on path space and formal series in a tensor algebra, under which a natural convolution of path functionals becomes an algebraic product of series. Applying it to a random unitary matrix-valued path development - the quantum path signature - we show that the governing planar loop equations take a non-commutative spectral form. We then extend the loop equations to a 1/N genus expansion, organised by topological recursion, and obtain a hierarchy of integral equations on path space for the corrections.

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