In the presence of spacetime torsion, the momentum components do not commute; therefore, in quantum field theory, summation over the momentum eigenvalues will replace integration over the momentum. In the Einstein–Cartan theory of gravity, in which torsion is coupled to spin, the separation between the eigenvalues increases with the magnitude of the momentum. Consequently, this replacement regularizes divergent integrals in Feynman diagrams with loops by turning them into convergent sums. In this article, we apply torsional regularization to the self-energy of a charged lepton in quantum electrodynamics. We show that torsion eliminates the ultraviolet divergence of the standard self-energy. We also show that the infrared divergence is absent. In the end, we calculate the finite bare masses of the electron, muon, and tau lepton: 0.4329MeV, 90.95MeV, and 1543MeV, respectively. These values constitute about 85% of the observed, re-normalized masses.

中文翻译：

---

自能和电子裸质量的扭转正则化


在存在时空扭转的情况下，动量分量不交换;因此，在量子场论中，动量特征值的求和将取代动量的积分。在 Einstein-Cartan 引力理论中，扭转与自旋耦合，特征值之间的间隔随着动量的大小而增加。因此，这种替换通过将 Feynman 图中的发散积分转换为收敛和来正则化它们。在本文中，我们将扭转正则化应用于量子电动力学中带电轻子的自能。我们表明，扭转消除了标准自能的紫外线发散。我们还表明红外发散是不存在的。最后，我们计算了电子、μ 子和 tau 轻子的有限裸质量：分别为 0.4329MeV、90.95MeV 和 1543MeV。这些值约占观测到的重新归一化质量的 85%。