The Schrödinger kernel of the twisted Laplacian and cyclic models

Molahajloo, Shahla; Wong, M. W.

doi:10.1007/s00013-010-0206-1

Cited by 3 publications

(1 citation statement)

References 12 publications

(14 reference statements)

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“…This has provided us with another way to recover the Berezin transforms attached to the generalized Bargmann spaces under consideration, which was constructed in [5,6] by means of Toeplitz operators. For related recent works in the literature, we should mention the references [26,27,28,29,30]. We have also established two other formulae expressing these Berezin transforms as functions of Euclidean Laplacian.…”

Section: Discussionmentioning

confidence: 95%

Coherent States Quantization for Generalized Bargmann Spaces with Formulae for Their Attached Berezin Transforms in Terms of the Laplacian on ℂ N

Mouayn

2011

J Fourier Anal Appl

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While dealing with a class of generalized Bargmann spaces, we rederive their reproducing kernels from the knowledge of an orthonormal basis by using an addition formula for Laguerre polynomials involving the disk polynomials. We construct for each of these spaces a set of coherent states to apply a coherent states quantization method. This provides us with another way to recover the Berezin transforms attached to these spaces. Finally, two new formulae representing these transforms as functions of the Euclidean Laplacian are established and a possible physics direction for the application of such formulae is discussed.

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Section: Discussionmentioning

confidence: 95%

Coherent States Quantization for Generalized Bargmann Spaces with Formulae for Their Attached Berezin Transforms in Terms of the Laplacian on ℂ N

Mouayn

2011

J Fourier Anal Appl

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Weyl transforms and solutions to Schrödinger equations for time-dependent Hermite operators

Kagawa

Wong

2012

J. Pseudo-Differ. Oper. Appl.

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Semiclassical limits of the Schrödinger kernels on the $$h$$ h -Heisenberg group

Kagawa

2014

J. Pseudo-Differ. Oper. Appl.

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The Schrödinger kernel of the twisted Laplacian and cyclic models

Abstract: We give a rigorous derivation of the integral kernel of the Schrödinger equation governed by the twisted Laplacian and give an interpretation in terms of cyclic models in physics.Mathematics Subject Classification (2010). 47F05, 47G30, 81Q05.

Cited by 3 publications

References 12 publications

Coherent States Quantization for Generalized Bargmann Spaces with Formulae for Their Attached Berezin Transforms in Terms of the Laplacian on ℂ N

Coherent States Quantization for Generalized Bargmann Spaces with Formulae for Their Attached Berezin Transforms in Terms of the Laplacian on ℂ N

Weyl transforms and solutions to Schrödinger equations for time-dependent Hermite operators

Semiclassical limits of the Schrödinger kernels on the $$h$$ h -Heisenberg group

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