论文标题
自由费点的科尔曼通讯
The Coleman correspondence at the free fermion point
论文作者
论文摘要
我们证明，所有耦合常数都存在$ \ mathbb {r}^2 $与$ \ mathbb {r}^2 $在$ \ mathbb {r}^2 $上相关的电荷和梯度字段的截断相关函数，所有耦合常数都均等于手性的大规模dirac fermions的手性密度和载体。这是科尔曼预测的一个例子，即无质量的正弦模型和大量的横跨模型是等效的（在上述相关函数的意义上）。我们的主要新颖性是，我们证明了这种对应关系，从无限体积模型的非替代性方案中的欧几里得路径积分开始。我们使用此通信表明，无质量正弦模型与$β=4π$衰减的相关函数呈指数型，并且相应的概率场是定位的。
We prove that the truncated correlation functions of the charge and gradient fields associated with the massless sine-Gordon model on $\mathbb{R}^2$ with $β=4π$ exist for all coupling constants and are equal to those of the chiral densities and vector current of free massive Dirac fermions. This is an instance of Coleman's prediction that the massless sine-Gordon model and the massive Thirring model are equivalent (in the above sense of correlation functions). Our main novelty is that we prove this correspondence starting from the Euclidean path integral in the non-perturative regime of the infinite volume models. We use this correspondence to show that the correlation functions of the massless sine-Gordon model with $β=4π$ decay exponentially and that the corresponding probabilistic field is localized.
