有效规范理论、重整化群和高温超导
Effective Gauge Theories, The Renormalization Group, and High-Temperature Superconductivity
摘要：
这些讲座作为一个介绍重整化群的方法，以有效场论，重点放在系统与费米表面。对于这样的系统，要求适当的激发相对于重整化群进行适当的标度，这直接导致了准粒子的重要概念以及大N_f处理与理论空间中重整化群之间的联系。在这样的处理中，N_f表示费米面以上的有效费米自由度的数量;这个数量大致与费米面的大小成正比。作为这些思想的一个应用，本文讨论了三维U（1）规范理论中的非平凡红外结构，以及在高温超导体正相物理中的应用，试图解释实验观察到的与费米液体行为的偏离。具体而言，直流电阻率的理论计算在有限的温度，$T$，并发现收购$O(1/N_f)$校正的线性$T$的行为。这种标度修正与最近在高温超导铜氧化物中的实验观察是一致的。
英文摘要：
These lectures serve as an introduction to the renormalization group approach to effective field theories, with emphasis on systems with a Fermi surface. For such systems, demanding appropriate scaling with respect to the renormalization group for the appropriate excitations leads directly to the important concept of quasiparticles and the connexion between large-N_f treatments and renormalization group running in theory space. In such treatments N_f denotes the number of effective fermionic degrees of freedom above the Fermi surface; this number is roughly proportional to the size of the Fermi surface. As an application of these ideas, non-trivial infra red structure in three dimensional U(1) gauge theory is discussed, along with applications to the normal phase physics of high-T_c superconductors, in an attempt to explain the experimentally observed deviations from Fermi liquid behaviour. Specifically, the direct current resistivity of the theory is computed at finite temperatures, $T$, and is found to acquire $O(1/N_f)$ corrections to the linear $T$ behaviour. Such scaling corrections are consistent with recent experimental observations in high T_c superconducting cuprates.
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