We study the Dirac propagator dressed by an arbitrary number N of photons by means of a worldline approach, which makes use of a supersymmetric $\mathcal{N}=1$ spinning particle model on the line, coupled to an external Abelian vector field. We obtain a compact off-shell master formula for the tree level scattering amplitudes associated to the dressed Dirac propagator. In particular, unlike in other approaches, we express the particle fermionic degrees of freedom using a coherent state basis, and consider the gauging of the supersymmetry, which ultimately amounts to integrating over a worldline gravitino modulus, other than the usual worldline einbein modulus which corresponds to the Schwinger time integral. The path integral over the gravitino reproduces the numerator of the dressed Dirac propagator.

我们通过世界线方法研究了由任意数量N个光子修饰的狄拉克传播子，该方法利用了超对称$\mathcal{N}=1$在线上的旋转粒子模型，耦合到外部阿贝尔矢量场。我们获得了一个紧凑的壳外主公式，用于与经过修饰的狄拉克传播子相关的树级散射幅度。特别是，与其他方法不同，我们使用相干状态基础表达粒子费米子自由度，并考虑超对称性的测量，这最终相当于在世界线引力模量上积分，而不是通常的世界线 einbein 模量对应施温格时间积分。gravitino 上的路径积分再现了穿着的狄拉克传播子的分子。