(Mis-)handling gauge invariance in the theory of the quantum Hall effect. I. Unifying action and the nu=1/2 state

We propose a unifying theory for both the integral and fractional quantum H all regimes. This theory reconciles the Finkelstein approach to localizatio n and interaction effects with the topological issues of an instanton vacuu m and Chern-Simons gauge theory. We elaborate on the microscopic origins of the effective action, and unravel a new symmetry in the problem with Coulo mb interactions which we name F invariance. This symmetry has a broad range of physical consequences which will be the main topic of future analyses. In the second half of this paper, we compute the response of the theory to electromagnetic perturbations at a tree-level approximation. This is applic able to the theory of ordinary metals as well as the composite fermion appr oach to the half-integer effect. Fluctuations in the Chern-Simons gauge fie lds are found to be well behaved only when the theory is F invariant. [S016 3-1829(99)13539-2].