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Comultiplication inABCD algebra and scalar products of bethe wave functions

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Abstract

The representation of scalar products of Bethe wave functions in terms of dual fields, proved by A. G. Izergin and V. E. Korepin in 1987, plays an important role in the theory of completely integrable models. The proof in [A. G. Izergin, Dokl. Akad. Nauk SSSR,297, No. 2, 331 (1987)] and [V. E. Korepin, Commun. Math. Phys.,113, 177–190 (1978)] is based on the explicit expression for the “senior” coefficient, which was guessed in the Izergin paper and then proved to satisfy some recurrent relations, which determine it unambiguously. In this paper we present an alternative proof based on direct computation. It uses the operation of comultiplication in the ABCD-algebra.

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Authors
  1. A. Mikhailov
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The Moscow State University, Moscow, Russia; Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 100, No. 1, pp. 113–118, July, 1994.

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Mikhailov, A. Comultiplication inABCD algebra and scalar products of bethe wave functions. Theor Math Phys 100, 886–889 (1994). https://doi.org/10.1007/BF01017327

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  • DOI: https://doi.org/10.1007/BF01017327

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