  The Uehling contribution to the Lamb shift can be computed exactly in terms
of the Uehling potential function. However derivations of this function are
complex involving avoiding divergences using intricate techniques from early
quantum field theory (QFT) or else more modern approaches using charge and mass
renormalization. In the present paper we derive the Uehling potential function
in a fairly conceptually straightforward way not involving renormalization in
which the vacuum polarization tensor is viewed as a Lorentz invariant 2-tensor
valued measure on Minkowski space. Furthermore we compute a complex matrix
valued potential function for the electron self-energy contribution to the Lamb
shift. The resulting potential function is derived in a conceptually simple way
not involving renormalization and can be used for higher order computations in
QFT involving multiple loops.
