后代算子的形状因子：自由域构造和反射关系
Form factors of descendant operators: Free field construction and reflection relations
摘要：
对sinh-Gordon模型和sine-Gordon模型中形状因子的自由场表示进行了修正，使其能描述后代算子的形状因子，这些形状因子是通过与场$ϕ(x)$相关联的Heisenberg代数的作用从指数算子$\e^{ıαϕ}$得到的.作为一个检查的有效性的建设，我们计数的运营商的数量定义的形状因子在每个水平在每个手性部门。另一种检查涉及所谓的反射关系，其在通气扇区中识别用于$α$的通用值的指数字段$\e^{ıαϕ}$和$\e^{ı(2α_0-α)ϕ}$的后代。我们证明了由所得到的形状因子族定义的算子满足这样的反射关系。本文还提出了一种将形状因子的构造推广到扭结扇区的方法。
英文摘要：
The free field representation for form factors in the sinh-Gordon model and the sine-Gordon model in the breather sector is modified to describe the form factors of descendant operators, which are obtained from the exponential ones, $\e^{ıαϕ}$, by means of the action of the Heisenberg algebra associated to the field $ϕ(x)$. As a check of the validity of the construction we count the numbers of operators defined by the form factors at each level in each chiral sector. Another check is related to the so called reflection relations, which identify in the breather sector the descendants of the exponential fields $\e^{ıαϕ}$ and $\e^{ı(2α_0-α)ϕ}$ for generic values of $α$. We prove the operators defined by the obtained families of form factors to satisfy such reflection relations. A generalization of the construction for form factors to the kink sector is also proposed.
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