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