Many Body

Many Body & Critical Phenomena

[Fall 2015 - MS Physics - IST - Lisbon]

Syllabus

0. Introduction

Course logistics

What are you going to lean? What is it useful for?

1. Particles and fields

Quantization

Statistical ensembles (review)

Methods I

2. Green's functions

Representation of quantum mechanics

Linear Response I

Green's functions

Canonical Formalism (finite and zero temperature)

3. Path Integrals

Methods II

Gaussian integrals

Bogoliubov transformations

Single particle path integral

Propagator of a single particle

Semi-classics and WKB

Wick's rotation

Double well potential - instantons

Coherent states

Bosonic

Fermionic

Many body path integral

Sources

Linear Response II

Legendre Transform

4, Perturbation theory

Diagrammatic expansion

Re-summation - Dyson equation

Luttinger-Ward and 2p irreducible formalism

5. Applications I - Bose Liquid

Superfluidity

6. Application II - Fermi-Liquid

Introduction

Fermi-Liquid theory

Instabilities

Non-Fermi liquids

Biblio

Main bibliography:

1. [A&S] Condensed Matter Field Theory.

Alexander Altland and Ben Simons , Cambridge University Press

Modern textbook emphasizing functional integrals techniques.

2. [M] Many-Particle Physics

Gerald D. Mahan, Plenum Press

Classical textbook. Response functions: Green's function and Kubo formalism.

3. [F&W] Quantum Thoery of Many-Particle Systems

A.L. Fetter and J.D. Walecka, McGraw-Hill

Another classical textbook.

Additional bibliography:

1. [AA] Interacting Electrons and Quantum Magnetism

Assa Auerbach, Springer Verlag

2. [D&S] Green's Function in Solid State Physics

Doniach and Sondheimer

3. [N&O] Quantum Many-Particle Systems

Negele and Orland

4. [AGD] Methods of Quantum Field Theory in Statistical Physics

Abrikosov, Gorkov and Dzyaloshinski

5. [EF] Field Theories of Condensed Matter Systems

E. Fradkin

6. Renormalization-group approach to interacting fermions

R. Shankar Rev. Mod. Phys. 66, 129 (1994)

7. [BS] Quantum Condensed Matter Field Theory, lecture notes Ben Simonshttp://www.tcm.phy.cam.ac.uk/~bds10/tp3/lectures.pdf

8. [P&S] An Introduction to Quantum Field Theory

Peskin and Schroeder

9. [B&F] Many-Body Quantum Theory in Condensed Matter Physics

H. Bruus and K. Flensberg