重整化群流中奇异Legendre变换的光滑化
Smoothing of Singular Legendre Transforms in Renormalization Group Flows
摘要：
我们考虑O（N）-对称势的对数奇异性的二阶导数。这一类包括BCS和Gross Neveu势。形式上，这些势的勒让德变换的精确重整化群方程似乎具有不明确的初始条件。我们表明，局部势的重整化群方程具有良好的初始条件，对数奇异性在流动中迅速平滑。我们的分析也提供了一个有效的方法进行数值研究。
英文摘要：
We consider O(N)-symmetric potentials with a logarithmic singularity in the second field derivative. This class includes BCS and Gross Neveu potentials. Formally, the exact renormalization group equation for the Legendre transform of these potentials seems to have ill-defined initial conditions. We show that the renormalization group equation for the local potential has well-defined initial conditions and that the logarithmic singularity is smoothed rapidly in the flow. Our analysis also provides an efficient method for numerical studies.
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