The wavefunction renormalization Z of a two-dimensional Fermi gas with
current-current interaction mediated by an unscreened transverse gaug
e held is discussed within a simple Hartree approximation for self-fie
ld effects. in the case of a three-dimensional gauge field, a critical
coupling strength is required before level crossing and strict orthog
onality occur. In the case of a two-dimensional gauge field, any finit
e coupling guarantees orthogonality beyond a critical system size.