Many-Body Theory, 214C
Spring 2019
MW,
2:00pm-3:20pm
RH 192
Instructor: Prof. Sasha Chernyshev
Office: RH 310F
Phone: (949)-824-6440
E-mail: sasha@uci.edu
Web page: http://www.physics.uci.edu/~sasha/
Technicalities:
Office Hours: open door
policy
Grading: Homework will be
assigned and collected every two weeks. Homework will constitute 80% of the grade.
Take-home final will be 20% of the grade.
Introduction
This course is about methods of Many-Body Theory,
i.e, a theory of non-relativistic particles mainly in the context of condensed matter problems.
Recommended Books
All the books are recomennded, but not required. Relevant pages
will be posted on the course web-site.
There is a lot of excellent books on
Many-Body Theory, each of them has its own strength.
Here is the list of my favorites and I may (or may not) use material from them
occasionally for the course.
- Quantum Field Theory for the Gifted Amateur,
by Tom Lancaster and Stephen Blundell,
A very new and exceptionally well-written book.
- Introduction to Many-Body Physics,
by Piers Coleman
It used to be an on-line book, at the moment it is going
to be "officially" published in October 2015 so the on-line link is down.
Excellent book with very detailed intro in many subjects.
- A. Fetter and J. Walecka, Quantum Theory of Many-Particle Systems,Dover
Publications, Inc., New York, 2003
An older classics, Stanford U course on Many-body.
- A. A. Abrikosov, L. P.
Gor'kov, and I. E. Dzyaloshinskii, Methods of Quantum Field Theory in
Statistical Physics, Dover Publications, Inc., New York,
1963.
also referred to as "The Bible" of many-body physics
...
- G. Mahan, Many-Particle Physics, Kluwer 2003
A very comprehensive book with lots of examples from condensed matter
physics ...
- L. D. Landau and E. M.
Lifshits, v.9, Statistical
Physics, II, Oxford
A great textbook. Main focus is on the Fermi-liquid theory and Bose
condensation/superfluidity
Here is a list of topics I am planning to cover in this course.
- Introduction
- on quasiparticles and general philosophy of many-body approaches,
[AGD]
- second quantization, number representation
- harmonic oscillator, phonons
- bosons, fermions, conserved particles, field operators
- quantization of operators
- Texts:
[QFTam],
[Coleman#1],
[Coleman#2],
[Mahan],
[FW],
[AGD]
- Canonical transformations
- Green's functions, Feynman
diagrams (T=0)
- Interaction representation, Wick theorem
[QFTam]
- S-matrix
- perturbation theory, Feynman diagrams
- poles, spectrum
- two-particle Green's Functions, vertex functions
- Texts:
[QFTam],
[Coleman#1],
[Coleman#2],
[Mahan],
[FW],
[LL],
[AGD]
- Examples
- impurity scattering, electron-phonon interaction
- electron-electron interaction, bound states,
Migdal's theorem
- (May or may not get there) Matsubara
diagram technique, T>0
- Analytical continuation
- Linear response theory
- Examples
Homework