Baxter's T-Q Relation and Bethe Ansatz of Discrete Quantum Pendulum and Sine-Gordon Model

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dc.creatorLin, Shao-shiung
dc.creatorRoan, Shi-shyr
dc.date2001-05-15
dc.date2002-08-30
dc.date.accessioned2026-07-07T04:11:40Z
dc.date.available2026-07-07T04:11:40Z
dc.descriptionUsing the Baxter's T-Q relation derived from the transfer matrix technique, we consider the diagonalization problem of discrete quantum pendulum and discrete quantum sine-Gordon Hamiltonian from the algebraic geometry aspect. For a finite chain system of the size L, when the spectral curve degenerates into rational curves, we have reduced Baxter's T-Q relation into a polynomial equation; the connection of T-Q polynomial equation with the algebraic Bethe Ansatz is clearly established . In particular, for L=4 it is the case of rational spectral curves for the discrete quantum pendulum and discrete sine-Gordon model. To these Baxter's T-Q polynomial equations, we have obtained the complete and explicit solutions with a detailed understanding of their quantitative and qualitative structure. In general the model possesses a spectral curve with a generic parameter. We have conducted certain qualitative study on the algebraic geometry of this high-genus Riemann surface incorporating Baxter's T-Q relation.
dc.description27 pages, Latex; Some reorganizations and improvement of presentations, and other minor changes
dc.identifierhttps://arxiv.org/abs/hep-th/0105140
dc.identifierhttp://arxiv.org/abs/hep-th/0105140
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/50678
dc.subjectHigh Energy Physics - Theory
dc.subjectStatistical Mechanics
dc.subjectMathematical Physics
dc.subjectAlgebraic Geometry
dc.subjectExactly Solvable and Integrable Systems
dc.titleBaxter's T-Q Relation and Bethe Ansatz of Discrete Quantum Pendulum and Sine-Gordon Model
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