Effective Field Theory and the Fermi Surface

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.

Figures (7)

• Figure 1: Fermi sea (shaded) with two low-lying excitations, an electron at ${\bf p} _1$ and a hole at ${\bf p} _2$.
• Figure 2: An electron of momentum ${\bf p} _1$ absorbs a phonon of large momentum ${\bf q}$ but remains near the Fermi surface.
• Figure 3: a) For two generic points near a two-dimensional Fermi surface, the tangents $\delta {\bf k} _i$ are linearly independent. b) For diametrically opposite points on a parity-symmetric Fermi surface, the tangents are parallel.
• Figure 4: a) Tree-level matrix element of current. b) One-loop correction which is marginal at ${\bf p} = {\bf p} '$. c) Two-loop correction which is marginal at ${\bf p} = {\bf p} '$.
• Figure 5: Scattering of electrons $( {\bf p} , E)$ and $(- {\bf p} , E)$ to $( {\bf p} ", E)$ and $(- {\bf p} ", E)$. a) Tree level. b) One loop.