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arXiv · 2608.02861

Topological Recursion and Quantum Path Signatures

Inês Aniceto·Thomas Cass·Samuel Crew
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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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Inês Aniceto, Thomas Cass, Samuel Crew. 2026-08-03. Topological Recursion and Quantum Path Signatures. https://arxiv.org/abs/2608.02861

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