Gauge theory of nonrelativistic fermions and its low-energy behavior Original Research Article

A system of (2+1)-dimensional nonrelativistic fermions with gauge interaction is studied by the renormalization-group analysis. Fluctuations of long-wavelength excitations of the gauge field are controlled as k2−b, where k is the magnitude of the momentum of a gauge boson and b is a parameter of the present system. This model is motivated by the work of Halperin, Lee and Read, which discussed a (2+1)-dimensional electron system in an external magnetic field at a filling factor of Landau level ν = 12. The β-function of gauge coupling and the anomalous dimension of a fermion are systematically calculated, in the sense of b − 1 expansion, both in the loop and the RPA-1/N expansions (where N is the number of species of fermions). The results are different in these two calculations. In the loop expansion, there appears a nontrivial IR fixed point of gauge coupling for b < 1, but the anomalous dimension of a fermion is vanishing. On the other hand, in the RPA calculation, renormalization of the gauge-fermion vertex does not occur, while the fermion wave function is renormalized because of a dissipative term in the dressed gauge propagator. These results are systematically understood by the Ward-Takahashi identity reflecting gauge invariance. Our calculations are compared with the recent work of Nayak and Wilczek.