由于20世纪80年代啁啾放大技术(CPA)的出现，激光强度指数级增长，量子电动力学预言的正负电子对产生所需要的临界场强期望在不久的将来会实现，从而可以直接验证光是否能直接转化为有质量的粒子。而在自然的高能反应中，往往伴随着统计效应，如在天体、黑洞演化中物质的产生与湮灭，总是用热平衡或非平衡的框架来描述。因此，讨论极端条件下物质的演化越发具有现实意义，特别是高温强场下粒子对产生。另外，时空的量子纠缠性质最近越来越被人们重视，其中环路复杂度就是描述时空演化的一个重要的物理量，它也可作为描述粒子对产生的特征量。因此，分析极端条件下粒子对产生或环路复杂度有助于我们利用激光来人为探究量子真空的性质。

本文研究热分布带电粒子在强外电磁场下粒子对的产生和它的环路复杂度。对于强外场，本文采用基于量子电动力学运动方程的强场Bogoliubov变换方法，此方法和有效拉式量方法的单圈计算精度一致，可表示为瞬子求和，能得到产生粒子对的谱分布。对热分布，本文采用热场动力学(TFD)中热场Bogoliubov变换, 此方法可用于描述粒子的实时热动力学过程，其对偶结构和共形场有一致性。通过结合这两个方法，我们得到了有初始粒子热分布和强外场下，粒子算符的总Bogoliubov变换，可表述为含时有相互作用的TFD态演化。进一步地，我们讨论了有限温度下强外场正负粒子对产生问题。另外，在此框架下，本文推导了强外场下真空态、单粒子TFD态以及正负粒子TFD态的环路复杂度形式，研究了它与正负粒子对产生之间的关系。

本文的创新点和主要结果有：

1.结合了强场和热场的Bogoliubov变换方法，讨论了有限温度下强外场中正负粒子对的产生，得到了初态是热正负粒子态、热光子态及它们的混合态时的形式结果，并运用到恒定电场情况下，分析了温度与粒子对产生数的关系：热光子促进粒子对产生，热费米子抑制粒子对产生，而热玻色子促进粒子对产生。

2.推导了强外场下的环路复杂度，得到了它与正负粒子对产生的关系，并证明单粒子的热演化部分和外场演化部分是耦合的，正负粒子的热演化部分和外场演化部分是非耦合的；并应用到Sauter 场情况下，得到了κ  = 2环路复杂度与脉冲时间τ正相关的关系。

Due to the advent of chirped amplification technology (CPA) in the 1980s, the intensity of laser light increased exponentially. The critical E-M field required for the creation of positronelectron pairs predicted by quantum electrodynamics will be realized in the near future, which will directly verify whether light can be converted into massive particles. In natural high-energy reactions, statistical effects are often accompanied. For example, the creation and annihilation of matter in the evolution of celestial bodies and black holes are always described in the framework of thermal equilibrium or non-equilibrium. It has more and more practical significance, especially in the creation of particle pairs under high temperature and strong fields. In addition, the quantum entanglement property of space-time has been paid more and more attention recently. Among them, the circuit complexity is an important physical quantity which describes the evolution of space-time. It can also be used as a characteristic quantity describing the particle pairs. Investigating pair production and circuit complexity in strong fields will help us to explore the properties of quantum vacuum with real lasers.

In this paper, the creation of charged pairs and its circuit complexity in the strong external electromagnetic fields are studied. For strong external fields, the strong-field Bogoliubov transform method based on the quantum electrodynamics motion equations is adopted，which is consistent with the single-loop accuracy of effective Lagrangian method. It is expressed as a sum of instantons so that spectral distribution of pairs can be obtained. For thermal distribution, Bogoliubov transform of the thermal field dynamics (TFD) is used here, which can describe the real-time thermodynamic process of particles. And its dual structure is consistent with conformal field. By combining these two methods, the total Bogoliubov transform of the operator of the particles with an initial thermal distribution and strong external field is obtained, which can be expressed as the evolution of time- dependent TFD states with interaction. Furthermore, the creation of positive and negative particle pairs in a strong external field at a finite temperature is discussed. Then, under this framework, the theory of circuit complexity of the TFD states in strong external fields is also established.

The innovations and important results are:

1.By taking advantages of the Bogoliubov transformation method of strong laser fields and thermal ones, the creation of positive and negative particle pairs in strong external fields at a finite temperature is studied. Theoretical frames when the initial state is thermal pairs state, thermal photon state and their mixed state are established. Further, these results are applied to the case of a constant electric field, then the relationship between temperature and number of pairs is explored. It is found that the number of the produced pairs will be promoted by thermal photons and bosons, while will be inhibited by thermal fermions.

2.Circuit complexity in strong external fields, and its relationship with the number of created pairs are derived. Then it is illustrated that for single particle the evolution part of the thermal field of is coupled with that of the external fields, while for particle pairs they are not coupled. Further, these results are applied to the case of Sauter field, and the positive correlation between κ  = 2 circuit complexity and pulse time τ is obtained.