Many-Body Theory, 214C
Spring 2007
MWF,
2:00pm-2:50pm
PSCB 210
Instructor: Dr. Sasha Chernyshev, Associate Professor
Office: FRH 2158
Phone: (949)-824-6440
E-mail: sasha@uci.edu
Web page: http://www.physics.uci.edu/faculty/chernyshev.html
Technicalities:
Office Hours: open door
policy
Grading: Homework will be
assigned each week and is due every third
week. Homework will constitute 50% of the grade.
Final exam (take-home) will be another 40%.
I will devote one lecture to the presentation on a many-body topic.
Presentation will be 10% of the grade.
Introduction
This course is about the methods of Many-Body Theory.
This means a theory of non-relativistic particles mainly in the context
of condensed matter problems.
Here is a list of topics I am planning to cover in this course.
- Introduction
- Second quantization, number representation
- bosons, fermions, spins, constrained operators
- Canonical transformations,
elements of representation theory
- Bogolyubov transformations, bosons, spin-waves
- Jordan-Wigner representation
- Hubbard operators, model, maping
- Green's functions, Feynman
diagrams (T=0)
- Interaction representation, Wick theorem
- perturbation theory, Feynman diagrams
- poles, spectrum
- two-particle Green's Functions, vertex functions
- Examples
- impurity scattering, electron-phonon interaction
- electron-electron interaction, bound states
- Matsubara
diagram technique, T>0
- Analytical continuation
- Linear response theory
- Examples
The above is a list of subjects I promise to talk about.
Here is the list of "other"
topics which I may (or may not) talk about, provided there is (or there
is not) enough time.
- Superconductivity,
diagrammatic methods
- Non-equilibrium processes, Keldysh diagram
technique
- Bosonization
- Elements of the renormalization
group method
Recommended Books
All the books are recomennded, but not required. In fact, it is hard to
find one which would fit into a 10 weeks course.
However, I'll try to follow most closely this one:
- A. Fetter and J. Walecka, Quantum Theory of Many-Particle Systems,Dover
Publications, Inc., New York, 2003
Another one, which was suggested for this course initially, might be a
little easier (and it has some fun pictures)
- R. D. Mattuck, A Guide to Feynman Diagrams in the
Many-Body Problem, Dover Publications, Inc., New York,
1992
Just for your information. There is plenty 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 them
occasionally for the course.
- 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"
...
- 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
- S. Doniach and Sondheimer, Green's Functions for Solid State
Physicists
- J. Negele and H. Orland, Quantum Many-Particle Systems
- E. N. Economou, Green's functions in Quantum Physics
There are also more modern books as well as on-line sources:
An evolving book by P. Coleman:
http://www.physics.rutgers.edu/~coleman/mbody/pdf/bk.pdf
Extra material
some pages from various books:
-- on quasiparticles and general philosophy of many-body approaches, 1
-- on second quantization and "identicity" of particles, 1, 2
-- on the problem of bose gas with repulsion, 1
-- superfluidity, qualitative discussion, 1
-- Jordan-Wigner transformation from Coleman's book, 1
Homeworks