标题： 闵可夫斯基空间中QED传播子的施温格- Dyson方程的表述 显示英文标题

标题： Formulating Schwinger--Dyson equations for QED propagators in Minkowski space

摘要： 施温格- Dyson 方程（SDEs）是量子场论（QFT）的 Green 函数的一组耦合积分方程。SDE 方法是求解强耦合 QFT 的解析非微扰方法。应用于量子色动力学（QCD）时，这种方法同样基于第一性原理，是格点 QCD 的解析替代方案。然而，n 点 Green 函数的 SDE 涉及 (n+1) 点 Green 函数（有时还包括 (n+2) 点函数）。因此，任何实际用于求解这无限耦合方程组的方法都需要截断方案。当将强耦合 QED 作为 QCD 的模型时，朴素的截断方案会违反规范理论的各种原则。这些原则包括规范不变性、规范协变性和乘法可重正化性。将维度正则化与传播子的谱表示相结合，可以得到 QED 传播子 SDE 的可处理截断方案形式，该形式有可能保留上述原则，并使在闵可夫斯基空间中获得解成为可能。 显示英文摘要

摘要： The Schwinger--Dyson equations (SDEs) are coupled integral equations for the Green's functions of a quantum field theory (QFT). The SDE approach is the analytic nonperturbative method for solving strongly coupled QFTs. When applied to QCD, this approach, also based on the first principle, is the analytic alternative to lattice QCD. However, the SDEs for the n-point Green's functions involves (n+1)-point Green's functions (sometimes (n+2)-point functions as well). Therefore any practical method for solving this infinitely coupled system of equations requires a truncation scheme. When considering strongly coupled QED as a modeling of QCD, naive truncation schemes violate various principles of the gauge theory. These principles include gauge invariance, gauge covariance, and multiplicative renormalizability. The combination of dimensional regularization with the spectral representation of propagators results in a tractable formulation of a truncation scheme for the SDEs of QED propagators, which has the potential to preserve the aforementioned principles and renders solutions obtainable in the Minkowski space.