Korff, C. (2016) From quantum Bäcklund transforms to topological quantum field theory. Journal of Physics A: Mathematical and Theoretical, 49(10), 104001. (doi: 10.1088/1751-8113/49/10/104001)
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Abstract
We derive the quantum analogue of a Bäcklund transformation for the quantized Ablowitz–Ladik chain, a space discretization of the nonlinear Schrödinger equation. The quantization of the Ablowitz–Ladik chain leads to the q-boson model. Using a previous construction of Baxter's Q-operator for this model by the author, a set of functional relations is obtained which matches the relations of a one-variable classical Bäcklund transform to all orders in ${\hslash }$. We construct also a second Q-operator and show that it is closely related to the inverse of the first. The multi-Bäcklund transforms generated from the Q-operator define the fusion matrices of a 2D TQFT and we derive a linear system for the solution to the quantum Bäcklund relations in terms of the TQFT fusion coefficients.
Item Type: | Articles |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Korff, Professor Christian |
Authors: | Korff, C. |
Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Research Group: | Integrable Systems and Mathematical Physics |
Journal Name: | Journal of Physics A: Mathematical and Theoretical |
Publisher: | IOP Publishing |
ISSN: | 1751-8113 |
ISSN (Online): | 1751-8121 |
Copyright Holders: | Copyright © 2016 IOP Publishing Ltd. |
First Published: | First published in Journal of Physics A: Mathematical and Theoretical 49(10): 104001 |
Publisher Policy: | Reproduced in accordance with the copyright policy of the publisher |
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