Light traveling in an electromagnetic field is not affected by the presence of the electromagnetic field in Maxwell electrodynamics, which is linear. However, in quantum electrodynamics, nonlinear terms are created in the effective action by quantum fluctuation and the propagation of light is affected by the external electromagnetic field. In Born-Infeld electrodynamics introduced to solve the divergence of the electromagnetic field at the origin, the permittivity and the permeability of vacuum in the presence of an external electromagnetic field are not one by non-linearity. We study the bending of a light ray passing a strong external electric field in generalized Born-Infeld electrodynamics, which includes the quantum effect. When a light ray moves around electrically charged objects like a charged black hole or an atomic nucleus, the path of light can be bent by the gradient of the effective index of refraction. We use the trajectory equation based on geometric optics for weak lensing, in which the impact parameter is large compared to the characteristic length of the Born-Infeld parameter, to compute the bending angle.

Keywords: Born-Infeld electrodynamics, Weak lensing, Trajectory equation