QED级数的最优项数及其在QED的condensed matter实现中的推论
Optimal number of terms in QED series and its consequence in condensed matter implementations of QED
摘要：
1952年戴森提出了一个简单而有力的论证，指出QED的微扰展开是渐近的。他的论点可以与卡拉塞卡的限制质量的恒星的稳定性对引力坍缩。结合这两个参数，我们估计QED级数的最佳项数为$3.1(137)^{3/2}\approx5000$。对于窄禁带半导体和Weyl半金属中的QED的凝聚态表现，最佳的项数是$80$左右，而在石墨烯中，微扰理论的实用性受到严重限制。
英文摘要：
In 1952 Dyson put forward a simple and powerful argument indicating that the perturbative expansions of QED are asymptotic. His argument can be related to Chandrasekhar's limit on the mass of a star for stability against gravitational collapse. Combining these two arguments we estimate the optimal number of terms of the QED series to be $3.1(137)^{3/2}\approx5000$. For condensed matter manifestations of QED in narrow band-gap semiconductors and Weyl semimetals the optimal number of terms is around $80$ while in graphene the utility of the perturbation theory is severely limited.
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