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Baxter Q-Operators and Representations of Yangians

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons2679

Meneghelli,  Carlo
Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons20717

Staudacher,  Matthias
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Volltexte (frei zugänglich)

1010.3699
(Preprint), 422KB

NPB850_148.pdf
(beliebiger Volltext), 453KB

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Zitation

Bazhanov, V. V., Frassek, R., Lukowski, T., Meneghelli, C., & Staudacher, M. (2011). Baxter Q-Operators and Representations of Yangians. Nuclear Physics B, 850, 148-174. doi:10.1016/j.nuclphysb.2011.04.006.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0012-CE86-7
Zusammenfassung
We develop a new approach to Baxter Q-operators by relating them to the theory of Yangians, which are the simplest examples for quantum groups. Here we open up a new chapter in this theory and study certain degenerate solutions of the Yang-Baxter equation connected with harmonic oscillator algebras. These infinite-state solutions of the Yang-Baxter equation serve as elementary, "partonic" building blocks for other solutions via the standard fusion procedure. As a first example of the method we consider sl(n) compact spin chains and derive the full hierarchy of operatorial functional equations for all related commuting transfer matrices and Q-operators. This leads to a systematic and transparent solution of these chains, where the nested Bethe equations are derived in an entirely algebraic fashion, without any reference to the traditional Bethe ansatz techniques.