Topological Recursion and Quantum Path Signatures

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.

Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th); Probability (math.PR); Quantum Physics (quant-ph)

arXiv:2608.02861 [math-ph]

(or arXiv:2608.02861v1 [math-ph] for this version)

https://doi.org/10.48550/arXiv.2608.02861 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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