\right\}\!, \label{eq:2}\end{aligned}$$ with $\hat{\mathcal{H}}_0 = \mathcal{H}_0(-i\vec\nabla)$ and $c_0=1/4\pi$. Here $\psi$ is a four-component spinor, but subsequently we will artificially add an additional $U(N_f)$ flavor index, which allows a check on our calculations by large $N_f$ methods; the physical case is $N_f=1$. Eq.  contains in addition to the three mass parameters, the Coulomb coupling constant $e$. For $e=0$, scale invariance is manifest, with the scaling dimensions $[x^{-1}]=1 \, , \, [\tau^{-1}]=z
\, , \, [\psi] = \frac{d}{2} \, , \, [\frac{1}{m}]=z-2$, $[\varphi]=(d+z-2)/2$. Here we introduce the dynamic critical exponent ($z$), which is naturally $z=2$ with $e=0$, but will become non-trivial with interactions.

Directly in the physical case $d=3$, the dimension of the coupling constant is $[e^2] =1$, so Coulomb interactions are strongly relevant. Therefore we employ the $\varepsilon=4-d$ expansion to control the RG analysis. As familiar from quantum electrodynamics, three one loop Feynmann diagrams contribute to leading order in $\varepsilon$: the fermion self-energy, boson self-energy, and vertex correction. Here we show that the relevance of Coulomb interactions signals, rather than a flow to strong coupling and a symmetry breaking instability, the formation of a new [*stable*]{} interacting fixed point, which describes the critical non-Fermi liquid LAB state (Abrikosov’s analysis tacitly assumes 