In both theory and practice, condensed matter physics is concerned with the physical properties of materials that are comprised of complex many-particle systems. Modeling the systems' behavior is essential to achieving a better understanding of the properties of these systems and their practical use in technology and industry.

Maximal knowledge about a many-particle system is gained by solving the Schrödingere quation. However, an exact solution of the Schrödinger equation is not possible, so resort is made to approximation schemes based on perturbation theory. It is generally true that, in order to properly describe the properties of an interacting many-particle system, perturbation theory must be carried out to infinite order. The best approach we have for doing so involves the use of Green's function and Feynman diagrams. Furthermore, much of our knowledge about a given complex system is obtained by measuring its response to an external probe, such as an electromagnetic field, a beam of electrons, or some other form of perturbation; its response to this perturbation is best described in terms of Green's function.

Two years ago, I set out to put together a guide that would allow advanced undergraduate and beginning graduate students in physics and electrical engineering to understand how Green's functions and Feynman diagrams are used to more accurately model complicated interactions in condensed matter physics.