# Tentative plan

*Note that this plan is subject to change.*

## Hors d'oeuvre

Mean-field theories

## Hedin's equations: the general formalism of Green's functions

References:

- Hedin, L. and S. O. Lundqvist. “Effects of Electron-Electron and Electron-Phonon Interactions on the One-Electron States of Solids”. in Solid State Physics 23 (1969) 1.
- refer to Solyom's book, Jishi book of diagrammatics, Bruus, advanced Kittel & Ziman for better connection to solid state theory.
- Pine’s “elementary excitations in solids”

Goals:

- understanding Green's function techniques in depth
- obtaining the know-how to analyse and physically interpret the results, such as spectral functions, self-energy, response functions, vertex corrections, etc.
- produce self-consistent diagrammatics
- understanding adiabatic continuity and Gell-Mann--Low theorem
- understanding the many-body results also in terms of the earlier wave-function approach, based on the single-particle picture; e.g., Hartree-Fock approximation, random phase approximation (RPA) and plasmons, Overhauser’s spin waves [Pine’s “elementary excitations in solids"]
- learn how to relate theory to experiments, and understand and interpret experimental results: e.g., XPS, ARPES, etc. refer to Jülich lecture notes

## Fundamentals of Fermi liquid theory as the paradigm of strongly interacting many-body systems

Goals:

– deriving the properties of a Fermi liquid

– Luttinger theorem

– topological view of a Fermi liquid

References:

refer to AGD book,

Mudry (esp. chp on topological Fermi liquid theory),

Martin's book

## Interacting bosonic systems:

Goals:

– quantum many-body understanding of electromagnetism: photons

– quantum optics fundamentals

– Bose-Einstein condensate and anomalous Green functions

References:

AGD book, Mudry, Jishi

## Transport properties

Goals:

– Linear response theory

– Meir-Wingreen formula

– Boltzmann equation

– Landauer-Bütticker formalism

References:

Bruus

Rammer

papers

## Functional-integral formalism fundamentals

– Hubbard-Stratonovich transformation

## Effective action formalism and conserving approximations

References:

Baym and Kadanoff paper

chapter by Bickers

Effective action formalism -> Bergerson's (?) review

Stefanucci and van Leuween: Luttinger-Ward functionals

BCS theory of Hassler and Morawetz

## Magnetism (esp. itinerant magnetism) and Kondo effect

Stoner model

Anderson model

Giamarchi lecture notes

Bell Lab guys on Kondo

Nozieres paper on X-ray problem

Kondo's review

## Non-equilibrium many-body theory

Goals:

Keldysh technique

refer to Jülich lecture notes

Master eq approach and Born-Markov approximation

## Breakdown of quantum phases and quantum phase transitions (beyond mean-field)

Goals:

– Renormalization group (RG) techniques

Kopietz book: Functional renormalization group

paper by Shankar on fermionic renormaliztion

paper by Hertz and Millis

## Exotic quantum phases

Goals:

– Breakdown of Fermi liquids and non-Fermi liquid theory

low-dimensional systems:

1D: Tomonaga-Luttinger liquid (Abelian Bosonization) -> Bruus, review by Brazilian J. Physics

2D: topological phases: Kosterlitz-Thouless transition