Theory of a Fermi-Liquid to Non-Fermi-Liquid Quantum Phase Transition in Dimensions $d>1$

We develop a theory for a generic instability of a Fermi liquid in dimension $d>1$ against the formation of a Luttinger-liquid-like state. The density of states at the Fermi level is the order parameter for the ensuing quantum phase transition, which is driven by the effective interaction strength. A scaling theory in conjunction with an effective field theory for clean electrons is used to obtain the critical behavior of observables. In the Fermi-liquid phase the order-parameter susceptibility, which is measurable by tunneling, is predicted to diverge for $1<d<3$.