Gravitational lensing in a plasma from worldlines

We study the deflection of light rays in a cold, non-magnetized plasma using the worldline framework. Starting from Synge's Hamiltonian formalism, we construct a position-space action and use it perturbatively to calculate light bending angles. In the homogeneous case, the action reduces to that of a massive particle, allowing us to extract the bending angle of light in the presence of the medium using a well-known analogy. For the inhomogeneous case, we consider a power law model and construct Feynman rules in time to compute the purely plasma-induced corrections to the bending angle at Next-to-Leading-Order (NLO).