共形场论中的广义Wick定理与Borcherds恒等式
Generalized Wick theorems in conformal field theory and the Borcherds identity
摘要：
作为Bais et. 1988年，在二维共形场论中的相互作用场的基础上，我们给出了一个新的围道积分公式，用于一个正常序算子及其右边的单个算子的算子乘积展开.与原来的反阶算子积的Wick定理非常相似，它把收缩即算子乘积展开的奇异部分表示为只有两项的围道积分，每项都是一个收缩和一个算子的乘积。我们讨论了这些公式和与顶点代数理论相关的量子场所满足的Borcherds恒等式之间的关系。
英文摘要：
As a counterpart of the well-known generalized Wick theorem by Bais et. al. in 1988 for interacting fields in two dimensional conformal field theory, we present a new contour integral formula for the operator product expansion of a normally ordered operator and a single operator on its right hand. Quite similar to the original Wick theorem for the opposite order operator product, it expresses the contraction i.e.the singular part of the operator product expansion as a contour integral of only two terms, each of which is a product of a contraction and a single operator. We discuss the relation between these formulas and the Borcherds identity satisfied by the quantum fields associated with the theory of vertex algebras.
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