精确计算量子场论的解析计算方法
Analytic Computing Methods for Precision Calculations in Quantum Field Theory
摘要：
综述了量子场论中单尺度观测量多圈修正的主要数学计算方法的现状，以及与之相关的数学数、函数空间和代数。目前，无质量的单标度量在QCD中可以解析地计算到4圈量级，单质量和双质量量可以解析地计算到3圈量级，零标度量可以解析地计算到5圈量级。计划测量的精度要求，特别是在FCC-ee，形成了重要的理论挑战，并将需要目前已知的方法的重要扩展。
英文摘要：
An overview is presented on the current status of main mathematical computation methods for the multi-loop corrections to single scale observables in quantum field theory and the associated mathematical number and function spaces and algebras. At present massless single scale quantities can be calculated analytically in QCD to 4-loop order and single mass and double mass quantities to 3-loop order, while zero scale quantities have been calculated to 5-loop order. The precision requirements of the planned measurements, particularly at the FCC-ee, form important challenges to theory, and will need important extensions of the presently known methods.
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