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Segal–Bargmann transform: the q-deformation

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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… Click to show full 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.

Keywords: transform deformation; bargmann transform; segal bargmann; deformed segal

Journal Title: Letters in Mathematical Physics
Year Published: 2017

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