标题： 关于 d > 2 维中保角主场的两种定义的等价性 显示英文标题

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

摘要： 共形主场在时空维度 d > 2 的共形场论中具有核心重要性。它们可以通过两种方式定义。第一种定义涉及场与共形群生成元之间的对易子；第二种定义根据有限共形变换下的行为来刻画主场。在现有文献中，这两种定义等价性的证明要么被省略，要么以很少的细节进行。本文对这两种定义进行了清晰简洁的回顾，并利用量子场论的一些基本结果和共形变换的基本性质，提供了它们等价性的一个简单而详细的证明。本文旨在作为共形场论入门课程的教学材料。 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. The paper is intended as a tutorial for an introductory lecture course in conformal field theory.