发表机构
Sapienza Università di Roma（罗马第一大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究通过量子逆散射方法，利用盒子长度重标度与在壳条件定义 sine-Gordon 模型的重整化方案，吸收截断依赖，并导出孤子与呼吸子质量，揭示可积性与重整化的关联。
AI 中文摘要
在量子逆散射方法中，sine-Gordon 模型在格点上求解，其连续极限和无穷体积极限只有在盒子长度被重新标度后才变得一致。我们证明，这种重新标度，辅以在壳条件，定义了一个重整化方案。对截断的整个依赖被吸收进一个因子 $Z_L$，该因子乘以盒子长度，其指数由顶点算子的标度维度固定；场和耦合常数 $\eta$ 均不被重整化，不引入任何减除标度，质量参数接受有限重整化，通过要求最轻的呼吸子具有线性化理论中玻色子的质量来确定。孤子和呼吸子的质量由单值算子的本征值作为不流动参数的函数得出，并在 $\eta\ ightarrow0$ 时还原为经典和半经典结果。特别是，质量比直接从正则化构造中产生，而格点参数与物理标度之间的关系被吸收进 $Z_L$，无需计算。该方案是理论的一种重新参数化，使得可积性与重整化之间的相互作用变得明确。我们将其与 Coleman 的正规序和共形微扰理论进行比较，并论证它可推广到具有质量谱的超局部可积理论，可能包括允许超局部格点正则化的渐近自由模型。
英文摘要
In the quantum inverse scattering method, the sine-Gordon model is solved on a lattice, and its continuum and infinite-volume limits become uniform only after the length of the box is rescaled. We show that this rescaling, supplemented by an on-shell condition, defines a renormalization scheme. The whole dependence on the cut-off is absorbed into a factor $Z_L$ multiplying the length of the box, with an exponent fixed by the scaling dimension of the vertex operator; neither the field nor the coupling $β$ is renormalized, no subtraction scale is introduced, and the mass parameter receives a finite renormalization, fixed by requiring that the lightest breather has the mass of the boson in the linearized theory. The soliton and breather masses follow from the eigenvalues of the monodromy operator as functions of parameters that do not run, and reduce to the classical and semiclassical results as $β\rightarrow0$. In particular, the mass ratios are produced directly from the regularized construction, while the relation between the lattice parameters and the physical scale is absorbed into $Z_L$ and never needs to be computed. The scheme is a reparameterization of the theory which makes explicit the interplay between integrability and renormalization. We compare it with Coleman's normal ordering and with conformal perturbation theory, and we argue that it extends to ultralocal integrable theories with a massive spectrum, possibly including asymptotically free models that admit an ultralocal lattice regularization.
