Analyticity and crossing properties of four-point function are investigated in conformal field theories in the frameworks of Wightman axioms. A Hermitian scalar conformal field, satisfying the Wightman axioms, is considered. The crucial role of microcausality in deriving analyticity domains is discussed and domains of analyticity are presented. A pair of permuted Wightman functions are envisaged. The crossing property is derived by appealing to the technique of analytic completion for the pair of permuted Wightman functions. The operator product expansion of a pair of scalar fields is studied and analyticity property of the matrix elements of composite fields, appearing in the operator product expansion, is investigated. An integral representation is presented for the commutator of composite fields where microcausality is a key ingredient. Three fundamental theorems of axiomatic local field theories; namely, PCT theorem, the theorem proving equivalence between PCT theorem and weak local commutativity and the edge-of-the-wedge theorem are invoked to derive a conformal bootstrap equation rigorously.

在Wightman公理的框架中，在共形场论中研究了四点函数的解析性和交叉性质。考虑了满足 Wightman 公理的 Hermitian 标量保形场。讨论了微观因果关系在推导分析性领域中的关键作用，并介绍了分析性领域。设想了一对置换的 Wightman 函数。交叉性质是通过对一对置换 Wightman 函数的解析完成技术推导出来的。研究了一对标量场的算子积展开，研究了出现在算子积展开中的复合场矩阵元的解析性。为复合场的交换子提供了一种积分表示，其中微因果关系是一个关键因素。公理局部场论的三个基本定理；即调用PCT定理、证明PCT定理与弱局部交换性等价的定理和楔形边定理，严格推导出保形自举方程。