Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-03-31
Phys.Lett. B357 (1995) 225-231
Physics
High Energy Physics
High Energy Physics - Theory
11 pages, plain tex, uses harvmac. Minor additions - version to be published in Physics Letters B
Scientific paper
10.1016/0370-2693(95)00913-6
For all Poincar\'e invariant Lagrangians of the form ${\cal L}\equiv f(F_{\mu\nu})$, in three Euclidean dimensions, where $f$ is any invariant function of a non-compact $U(1)$ field strength $F_{\mu\nu}$, 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 Wilson's renormalization group by neglecting all higher derivative terms $\sim \partial^nF$ in ${\cal L}$, 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-$T_c$ superconductivity is briefly discussed.
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