Abstract :
For all Poincaré invariant Lagrangians of the form L ≡ f(Fμν), in three Euclidean dimensions, where f is any invariant function of a non-compact U(1) field strength Fμν, we find that the only continuum limit (described by just such a gauge field) is that of free field theory: First we approximate a gauge invariant version of Wilsonʹs renormalization group by neglecting all higher derivative terms ∼ ∂nF in L, but allowing for a general non-vanishing anomalous dimension. Then we prove analytically that the resulting flow equation has only one acceptable fixed point: the Gaussian fixed point. The possible relevance to high-Tc superconductivity is briefly discussed.
