本文利用 AdS/CFT 对偶的基本原理研究了 boundary 上带电标量场在有限温度和有限化学势的条件下类空两点间的两点关联函数。我们采用了“Feynman’s worldline”方法，通过测地线近似将两点关联函数的计算转化为了 RN-AdS 黑洞背景下的在壳作用量计算。我们从“粒子”作用量出发导出了其运动方程，并且利用伪谱法（pseudo-spectral method）得到了粒子经典轨道的数值解，并计算了重正化作用量，由此给出了 boundary 上的两点关联函数及其对不同参数的依赖关系。
       本文的创新型在于: (1) 通过 AdS/CFT 对偶和“Feynman’s worldline”方法将无法用通常的微扰方式进行计算的强耦合场的两点关联函数转化为对粒子的经典路径作用量。 (2) 首次讨论了带电标量场在有限温度和有限化学势下两点关联函数。
 

        We use the AdS/CFT correspondence to study the two-point correlation function of charged scalar field at a scenario of finite temperature and chemical potential. Feynman’s worldline formalism and geodesic approximation are used. The calculation of the two-point correlation function is transformed into the calculation of renormalized action of a charged particle along its classical trajectory, which is given by our pseudo-spectral method calculation. We present the behavior of the two-point correlation function and its dependence on different parameters.
        The innovations of this article are as follows:(1)The two-point correlation functions are usually difficult to calculate especially in a strongly correlated system. We use AdS/CFT correspondence to make this calculation possible through a medium of on-shell action calculation. (2) This is the first time that the two-point correlation function of charged scalar in finite temperature and chemical potential has been given.