Nonrelativistic and Relativistic Coulomb Amplitude as the Matrix Element of a Rotation inO(4,2)

Abstract

It is shown that the Coulomb amplitude is the matrix element of the group element $e^{\mathrm{i}(\theta +\pi )\mathrm{J}2\mathrm{}}$ evaluated in a continuous basis in $\mathrm{SO}(4,2)\mathrm{}$. The method is applied to the relativistic Kepler problem without spins, but with the recoil corrections included. The form of the amplitude for this case is believed to be new.