Differential equations and integrable models: the SU(3) case
Differential equations and integrable models: the SU(3) case
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微分方程和可积模型：SU(3) 情况
DOI：
10.1016/s0550-3213(99)00791-9
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
R. Tateo
中科院分区：
文献类型：
--
作者：
P. Dorey;R. Tateo
我们展示了无质量a2（2）可积量子场论与某个三阶常微分方程之间的关系，从而扩展了最近将无质量sine-Gordon模型与薛定谔方程联系起来的结果。这形成了一个更一般的对应关系的一部分，涉及A2-相关的贝特系统和三阶微分方程。一个非线性积分方程的广义谱问题的推导，并进行了一些数值检查。讨论了对偶性质，并提出了非线性方程的一个简单变体作为描述受算子φ12、φ 21和φ15扰动的最小共形场论的有限体积基态能量的候选者。这是检查对以前的结果得到的热力学贝特anastrophic。
We exhibit a relationship between the massless a2(2)integrable quantum field theory and a certain third-order ordinary differential equation, thereby extending a recent result connecting the massless sine-Gordon model to the Schrödinger equation. This forms part of a more general correspondence involving A2-related Bethe ansatz systems and third-order differential equations. A non-linear integral equation for the generalised spectral problem is derived, and some numerical checks are performed. Duality properties are discussed, and a simple variant of the non-linear equation is suggested as a candidate to describe the finite volume ground state energies of minimal conformal field theories perturbed by the operators φ12, φ21and φ15. This is checked against previous results obtained using the thermodynamic Bethe ansatz.