标题： 关于QED中电子自能的三环计算 显示英文标题

标题： On the electron self-energy to three loops in QED

摘要： 我们计算量子电动力学中的电子自能，在椭圆类型核的迭代积分中达到三环。 我们使用微分方程方法，并结合一个$\epsilon$-因子化基，这使我们能够对所有维度调节器阶数中的迭代积分中出现的微分形式进行全面控制。 我们得到了简洁的解析表达式，我们提供了广义级数展开表示，使我们能够对电子动量平方的所有值进行数值计算。 作为副产品，我们也获得了在壳极限$p^2 = m^2$下自能的$\epsilon$-重求和结果，我们利用这些结果重新计算了已知的在壳方案中的三环重整化常数。 显示英文摘要

摘要： We compute the electron self-energy in Quantum Electrodynamics to three loops in terms of iterated integrals over kernels of elliptic type. We make use of the differential equations method, augmented by an $\epsilon$-factorized basis, which allows us to gain full control over the differential forms appearing in the iterated integrals to all orders in the dimensional regulator. We obtain compact analytic expressions, for which we provide generalized series expansion representations that allow us to evaluate the result numerically for all values of the electron momentum squared. As a by product, we also obtain $\epsilon$-resummed results for the self-energy in the on-shell limit $p^2 = m^2$, which we use to recompute the known three-loop renormalization constants in the on-shell scheme.