Scalar-QED h-corrections to the coulomb potential

The leading long-distance 1-loop quantum corrections to the Coulomb potenti al are derived for scalar QED and their gauge-independence is explicitly ch ecked. The potential is obtained from the direct calculation of the 2-parti cle scattering amplitude, taking into account all relevant 1-loop diagrams. Our investigation should be regarded as a first step towards the same prog ramme for effective Quantum Gravity. In particular, with our calculation in the framework of scalar QED, we are able to demonstrate the incompleteness of some previous studies concerning the Quantum Gravity counterpart.