General principles of quantum field theory imply that there exists an operator product expansion (OPE) for Wightman functions in Minkowski momentum space that converges for arbitrary kinematics. This convergence is guaranteed to hold in the sense of a distribution, meaning that it holds for correlation functions smeared by smooth test functions. The conformal blocks for this OPE are conceptually extremely simple: they are products of 3-point functions. We construct the conformal blocks in 2-dimensional conformal field theory and show that the OPE in fact converges pointwise to an ordinary function in a specific kinematic region. Using microcausality, we also formulate a bootstrap equation directly in terms of momentum space Wightman functions.

中文翻译：

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共形场论中的收敛动量空间 OPE 和自举方程

量子场论的一般原理意味着存在一个 Wightman 函数在 Minkowski 动量空间中的算子乘积展开 (OPE)，该函数收敛于任意运动学。这种收敛在分布的意义上保证成立，这意味着它适用于被平滑测试函数涂抹的相关函数。这个 OPE 的保形块在概念上非常简单：它们是 3 点函数的产物。我们在二维共形场理论中构建了共形块，并表明 OPE 实际上在特定运动学区域中逐点收敛到普通函数。使用微观因果关系，我们还直接根据动量空间 Wightman 函数制定了自举方程。