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arXiv · 1501.04508

Orthogonal polynomials, Laguerre Fock space and quasi-classical asymptotics

S. Twareque Ali·Miroslav Englis
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Abstract

Continuing our earlier investigation of the Hermite case [J. Math. Phys. 55 (2014), 042102], we study an unorthodox variant of the Berezin-Toeplitz quantization scheme associated with Laguerre polynomials. In particular, we describe a "Laguerre analogue" of the classical Fock (Segal-Bargmann) space and the relevant semi-classical asymptotics of its Toeplitz operators; the former actually turns out to coincide with the Hilbert space appearing in the construction of the well-known Barut-Girardello coherent states. Further extension to the case of Legendre polynomials is likewise discussed.

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S. Twareque Ali, Miroslav Englis. 2015-01-19. Orthogonal polynomials, Laguerre Fock space and quasi-classical asymptotics. https://arxiv.org/abs/1501.04508

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