标题： 非紧致纯规范QED在3D中是自由的 显示英文标题

标题： Non-Compact Pure Gauge QED in 3D is Free

摘要： 对于所有形式为${\cal L}\equiv f(F_{\mu\nu})$的保庞加莱拉格朗日量，在三维欧几里得空间中，其中$f$是非紧致$U(1)$场强$F_{\mu\nu}$的任意不变函数，我们发现唯一的连续极限（仅由这样的规范场描述）是自由场论：首先我们通过忽略${\cal L}$中的所有高阶导数项$\sim \partial^nF$来近似威尔逊重正化群的规范不变版本，但允许存在一般的非零反常维数。然后我们分析证明了所得的流方程只有一个可接受的固定点：高斯固定点。可能与高$T_c$超导性相关的讨论简要提及。 显示英文摘要

摘要： 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.