A. Zee, Quantum Field Theory in a Nutshell · Problem VI.7.1

Field Theory Redux

Physics — QFT

Problem

Work out the field theory that will allow you to study Anderson localization. [Hint: Consider the object

\left\langle \frac{1}{z - H} \right\rangle (x, y) \left\langle \frac{1}{w - H} \right\rangle (y, x)

for two complex numbers

z

and

w

. You will have to introduce two sets of replica fields, commonly denoted by

\phi_a^+

and

\phi_a^-

.] {Notation:

[1/(z - H)](x, y)

denotes the

xy

element of the matrix or operator

[1/(z - H)]