  We investigate 1-loop contributions to the 2- and 4-point correlation
functions within a theory for fermions with mass dimension one with a simple
quartic self-interaction term. The 1-loop divergence appearing the self-energy
function can be consistently absorbed by renormalization of the mass parameter.
In the case of the (1PI) 4-point correlation function, there is a surprising
cancellation of divergences coming from different diagrams, leading to a finite
1-loop result. The inclusion of a complete basis of four-fermion interactions
is discussed.
