标题： 在d > 2维中两个共形原初场定义的等价性 显示英文标题

标题： On the equivalence of two definitions of conformal primary fields in d > 2 dimensions

摘要： 共形原初场在具有$d>2$个时空维度的共形场论中起着核心作用。 它们可以有两种定义方式。 一种定义涉及场与共形群生成元之间的对易子；另一种定义则根据场在有限共形变换下的行为来表征一个原初场。 在现有文献中，这两种定义等价性的证明要么被省略，要么进行得不够详细。 在本文中，我们对这两种定义进行了清晰简洁的综述，并利用一些量子场论的最小结果和共形变换的基本性质，提供了一个简单且详细的等价性证明。 显示英文摘要

摘要： Conformal primary fields are of central importance in a conformal field theory with $d>2$ spacetime dimensions. They can be defined in two ways. A first definition involves commutators between the field and the generators of the conformal group; a second definition characterizes a primary field according to its behavior under a finite conformal transformation. In the existing literature, the proof of the equivalence of the definitions is either omitted or carried out with little details. In this paper we present a clear and concise review of the two definitions and provide a simple and detailed proof for their equivalence, using some minimal results from quantum field theory and basic properties of conformal transformations.