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Nested Bethe Ansatz and Finite Dimensional Canonical Commutation Relations

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Alex Kasman

Mathematical Physics · Submitted 24 Apr 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this note, solutions to the rational nested Bethe ansatz (RNBA) equations are constructed using the ``completed Calogero-Moser phase space'' of matrices which satisfy a finite dimensional analogue of the canonical commutation relationship.

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arXiv IDmath-ph/0004030 (version 1)
Pith IDGJX5NWKZ, Pith's permanent record of this paper and its review
CitationAlex Kasman. "Nested Bethe Ansatz and Finite Dimensional Canonical Commutation Relations." arXiv:math-ph/0004030 (2000). https://pith.science/paper/GJX5NWKZ
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,593 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.17 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; .

Recent interest in discrete, classical integrable systems has focused on their connection to quantum integrable systems via the Bethe equations. In this note, solutions to the rational nested Bethe ansatz (RNBA) equations are constructed using the ``completed Calogero-Moser phase space'' of matrices which satisfy a finite dimensional analogue of the canonical commutation relationship. A key feature is the fact that the RNBA equations are derived only from this commutation relationship and some elementary linear algebra. The solutions constructed in this way inherit continuous and discrete symmetries from the CM phase space.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 Recent interest in discrete, classical integrable systems has focused on their connection to quantum integrable systems via the Bethe equations. background 1.00 0.04 0.03 asserted 1.00
s1 In this note, solutions to the rational nested Bethe ansatz (RNBA) equations are constructed using the ``completed Calogero-Moser phase space'' of matrices which satisfy a finite dimensional analogue of the canonical commutation relationship. contribution 0.84 0.94 0.64 asserted 1.00
s2 A key feature is the fact that the RNBA equations are derived only from this commutation relationship and some elementary linear algebra. method 0.31 0.87 0.29 asserted 1.00
s3 The solutions constructed in this way inherit continuous and discrete symmetries from the CM phase space. result 0.78 0.85 0.19 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.77 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original abstract

Recent interest in discrete, classical integrable systems has focused on their connection to quantum integrable systems via the Bethe equations. In this note, solutions to the rational nested Bethe ansatz (RNBA) equations are constructed using the ``completed Calogero-Moser phase space'' of matrices which satisfy a finite dimensional analogue of the canonical commutation relationship. A key feature is the fact that the RNBA equations are derived only from this commutation relationship and some elementary linear algebra. The solutions constructed in this way inherit continuous and discrete symmetries from the CM phase space.

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