Semiclassical calculation of the photon propagator in two-dimensional scalar QED

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Abstract
This paper proposes a new semiclassical approach for calculating closed-loop quantities in scalar QED. This is carried through by the replacement of field degrees of freedom with particle coordinates, and then expanding about classical trajectories which dominate the theory. The one-charged-scalar closed-loop contribution to the photon propagator in two-dimensional scalar QED is calculated using this method. The semiclassical approximation developed gives the asymptotic behavior of the large-order terms in the perturbation expansion of the one-loop contribution to the photon self-energy.