Abstract
Because classical electrodynamics is linear, the vacuum is unique and trivial. In a classical vacuum, the speed of light is constant. In quantum electrodynamics, the vacuum expectation value of the electromagnetic current can be non-zero due to non-charge-like sources, like electric fields, magnetic fields, gravitational fields, temperature fields, etc. We consider the velocity shift of light due to the vacuum polarization effect of quantum electrodynamics when the temperature is finite. The speed of light in this non-trivial vacuum is different from that in a trivial vacuum at zero temperature. This means that the index of refraction is not one. We set up a model to find the trajectory and the bending angle of a light ray when the index of refraction has a gradient. We compute the bending angles when the gradient is spherically symmetric and when it is cylindrically symmetric. For a magnetized neutron star, We compare that bending angle with the bending angles caused by gravitation and electromagnetic field.
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