From quantum Bäcklund transforms to topological quantum field theory

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
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Korff, Dr 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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