Effective Gauge Theories, The Renormalization Group, and High-Temperature Superconductivity

Details Effective Gauge Theories, The Renormalization Group, and High-Temperature Superconductivity Effective Gauge Theories, The Renormalization Group, and High-Temperature Superconductivity

1998-10-23

arxiv.org/abs/cond-mat/9810324v3

Acta Phys.Polon. B29 (1998) 3819-3870

Physics

Condensed Matter

38 pages LATEX, figures incorporated (incorrect citation ref. [3] corrected; no other changes)

Scientific paper

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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