Variational method in relativistic quantum field theory without cutoff
Variational method in relativistic quantum field theory without cutoff
复制标题
无截止相对论量子场论中的变分法
作者：
A. Tilloy
变分方法是非微扰求解多体量子问题的有力方法。然而，在相对论量子场论(QFT)的背景下，它需要满足费曼概述的三个看似不相容的要求：可扩展性、可计算性和缺乏紫外线敏感性。在实践中，变分方法打破了这三种方法中的一种，这意味着需要有IR或UV截止。在这封信中，我介绍了在1+1维上联合满足3个条件的连续矩阵乘积态的一个相对论修正。我将它应用于自相互作用标量场，没有紫外线截止，直接在热力学极限下。数值结果表明，误差在参数个数上比任何幂定律减小得更快，而代价仍然只是多项式。
The variational method is a powerful approach to solve many-body quantum problems non perturbatively. However, in the context of relativistic quantum field theory (QFT), it needs to meet 3 seemingly incompatible requirements outlined by Feynman: extensivity, computability, and lack of UV sensitivity. In practice, variational methods break one of the 3, which translates into the need to have an IR or UV cutoff. In this letter, I introduce a relativistic modification of continuous matrix product states that satisfies the 3 requirements jointly in 1+1 dimensions. I apply it to the self-interacting scalar field, without UV cutoff and directly in the thermodynamic limit. Numerical evidence suggests the error decreases faster than any power law in the number of parameters, while the cost remains only polynomial.