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Darboux-Bäcklund Transformations for Spin-Valued Linear Problems

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Quantum Theory and Symmetries

Part of the book series: CRM Series in Mathematical Physics ((CRM))

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Abstract

Motivated by geometry of submanifolds we develop an algebraic construction of Darboux transformations using Clifford numbers and Spin groups. Eigenvalues parameterizing solitons, usually computed as zeros of determinants, are identified as zeros of the spinor norm. Reduction groups (loop groups) for Spin-valued linear problems are identified with involutions in Clifford algebras.

This paper is dedicated to Prof. Decio Levi on the occasion of his 70th birthday.

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Authors and Affiliations

  1. University of Bialystok, Faculty of Physics, Białystok, Poland

    Jan L. Cieśliński

Authors
  1. Jan L. Cieśliński
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Correspondence to Jan L. Cieśliński .

Editor information

Editors and Affiliations

  1. Département de physique, Université de Montréal, Montréal, QC, Canada

    M. B. Paranjape

  2. Département de physique, Université de Montréal, Montréal, QC, Canada

    Richard MacKenzie

  3. Department of Mathematics and Physics, SUNY Polytechnic Institute, Utica, NY, USA

    Zora Thomova

  4. Department of Mathematics and Statistics, Université de Montréal, Montréal, QC, Canada

    Pavel Winternitz

  5. Département de physique, Université de Montréal, Montréal, QC, Canada

    William Witczak-Krempa

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Cieśliński, J.L. (2021). Darboux-Bäcklund Transformations for Spin-Valued Linear Problems. In: Paranjape, M.B., MacKenzie, R., Thomova, Z., Winternitz, P., Witczak-Krempa, W. (eds) Quantum Theory and Symmetries. CRM Series in Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-55777-5_3

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