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Static potential in scalar QED$_3$ with non-minimal coupling

D. Dalmazi·Elias L. Mendonca
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Abstract

Here we compute the static potential in scalar $QED_3$ at leading order in $1/N_f$. We show that the addition of a non-minimal coupling of Pauli-type ($\eps j^μ\partial^νA^α$), although it breaks parity, it does not change the analytic structure of the photon propagator and consequently the static potential remains logarithmic (confining) at large distances. The non-minimal coupling modifies the potential, however, at small charge separations giving rise to a repulsive force of short range between opposite sign charges, which is relevant for the existence of bound states. This effect is in agreement with a previous calculation based on M$\ddot{o}$ller scattering, but differently from such calculation we show here that the repulsion appears independently of the presence of a tree level Chern-Simons term which rather affects the large distance behavior of the potential turning it into constant.

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D. Dalmazi, Elias L. Mendonca. 2006-08-30. Static potential in scalar QED$_3$ with non-minimal coupling. https://doi.org/10.1088/0305-4470%2F39%2F35%2F010

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