Effective Field Theory and the Fermi Surface

TL;DR

This paper introduces effective field theory methods and applies them to derive the low-energy theory of Fermi liquids, highlighting the need for alternative theories for high-temperature superconductors.

Contribution

It provides a derivation of the Landau Fermi liquid theory using effective field theory and discusses its limitations for high-$T_c$ superconductors.

Findings

Derivation of Fermi liquid theory via effective field theory

Explanation of why high-$T_c$ superconductors require different models

Clarification of low-energy excitations in conductors

Abstract

This is an introduction to the method of effective field theory. As an application, I derive the effective field theory of low energy excitations in a conductor, the Landau theory of Fermi liquids, and explain why the high-$T_c$ superconductors must be described by a different effective field theory.