论文标题
全球形式主义中的一环振幅
One-loop Amplitudes in the Worldline Formalism
论文作者
论文摘要
我们总结了将世界形式主义应用于单环N点振幅的分析计算时的最新进展。这种受弦乐启发的方法适应了标准Feynman图方法的某些计算效率，最著名的是提供主公式，这些公式与图表相比仅由外部腿部和/或内部传播器的位置差异。我们说明了标量和旋转QED中n-Photon振幅的低能限制所涉及的数学挑战，然后提出了一种算法，该算法原则上解决了这个问题，因为在PHI^3理论中，N-Point振幅更加困难的情况下，N-Point振幅更加困难。该方法基于逆导数的代数在周期性函数的希尔伯特空间与常数函数正交的空间中，其中伯努利数字和多项式起着核心作用。
We summarize recent progress in applying the worldline formalism to the analytic calculation of one-loop N-point amplitudes. This string-inspired approach is well-adapted to avoiding some of the calculational inefficiencies of the standard Feynman diagram approach, most notably by providing master formulas that sum over diagrams differing only by the position of external legs and/or internal propagators. We illustrate the mathematical challenge involved with the low-energy limit of the N-photon amplitudes in scalar and spinor QED, and then present an algorithm that, in principle, solves this problem for the much more difficult case of the N-point amplitudes at full momentum in phi^3 theory. The method is based on the algebra of inverse derivatives in the Hilbert space of periodic functions orthogonal to the constant ones, in which the Bernoulli numbers and polynomials play a central role.
