J. Frohlich et al., THE EFFECTIVE GAUGE FIELD ACTION OF A SYSTEM OF NONRELATIVISTIC ELECTRONS, Communications in Mathematical Physics, 173(2), 1995, pp. 417-452
We consider a system of free, non-relativistic electrons at zero tempe
rature and positive density, coupled to an arbitrary, external electro
magnetic vector potential, A. By integrating out the electron degrees
of freedom we obtain the effective action for A. We show that, in the
scaling limit, this effective action is quadratic in A and can be view
ed as an integral over the Fermi sphere of effective actions of (1 + 1
)-dimensional, chiral Schwinger models. We use this result to elucidat
e Luther-Haldane bosonization of systems of non-relativistic electrons
. We also study systems of weakly coupled interacting electrons for wh
ich the BCS channel is turned off. Using the quadratic dependence of t
he effective action on A, we show that, in the scaling limit, the RPA
yields the dominant contribution.