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arXiv · 1703.07388

Segal-Bargmann transform: the $q$-deformation

Guillaume Cébron·Ching-Wei Ho
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Abstract

We give identifications of the $q$-deformed Segal-Bargmann transform and define the Segal-Bargmann transform on mixed $q$-Gaussian variables. We prove that, when defined on the random matrix model of Śniady for the $q$-Gaussian variable, the classical Segal-Bargmann transform converges to the $q$-deformed Segal-Bargmann transform in the large $N$ limit. We also show that the $q$-deformed Segal-Bargmann transform can be recovered as a limit of a mixture of classical and free Segal-Bargmann transform.

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Guillaume Cébron, Ching-Wei Ho. 2017-03-21. Segal-Bargmann transform: the $q$-deformation. https://doi.org/10.1007/s11005-017-1039-7

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