Using the fermionic basis discovered in the 6-vertex model, we derive exact formulas for the expectation values of local operators of the sine-Gordon theory in any eigenstate of the Hamiltonian. We tested our formulas in the pure multi-soliton sector of the theory. In the ultraviolet limit, we checked our results against Liouville 3-point functions, while in the infrared limit, we evaluated our formulas in the semi-classical limit and compared them up to 2-particle contributions against the semi-classical limit of the previously conjectured LeClair-Mussardo type formula. Complete agreement was found in both cases.

中文翻译：

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正弦-戈登模型中的有限体积期望值

使用在 6 顶点模型中发现的费米子基，我们推导出正弦-戈登理论的局部算子在哈密顿量的任何本征态中的期望值的精确公式。我们在理论的纯多孤子部分测试了我们的公式。在紫外极限中，我们根据 Liouville 3 点函数检查了我们的结果，而在红外极限中，我们在半经典极限中评估了我们的公式，并将它们与 2 粒子贡献与之前推测 LeClair-Mussardo 型公式。在这两种情况下都发现完全一致。