Many Body Physics

Instructor:

E.S. Swanson
404 Allen Hall
4-9057       swansone@pitt.edu     http://fafnir.phyast.pitt.edu/IQM/

class meets Mondays and Wednesdays 11:00 - 12:15, 419 Allen Hall.

Office Hours: I will keep no official hours, drop in any time!

required text:

A. Fetter and J.D. Walecka, Quantum Theory of Many Particle Systems. ($25 at Barnes and Noble)

Additional texts:

Some good introductory texts:

R.D. Mattuck, A Guide to Feynman Diagrams in the Many-Body Problem
N.H. March, W.H. Young, and S. Sampanthar, The Many-Body Problem in Quantum Mechanics
R. Landau, Quantum Mechanics II

And some more advanced texts:

Marking Scheme: to be discussed in class.

Syllabus:

Introduction [MYS ch1, FW ch1, M ch0]
- many particle systems, single particle states, Fermi sea, Hartree mean field method
Second Quantization [MYS ch3, FW ch1, L ch19+26, M ch7]
- occupation number formalism, one body and two body operators, fermions and bosons, canonical transformations, particle-hole formalism, field operators
Perturbation Theory and Green's Functions [MYS ch4+10, FW ch 3, L ch, M ch8-10]
- Brillouin-Wigner and Rayleigh-Schroedinger perturbation theory, Goldstone theorem, adiabatic switching, time evolution, scattering theory, Wick's theorem, Green's functions, propagators, spectral function, Dyson equations
Fermi Fluids [FW Ch 4+5, M ch 12+13, MYS ch5]
- Coulomb screening, Gell-Mann -- Brueckner theory, ring diagrams, collective modes and plasmons, effective mass and renormalization, particle lifetimes, random phase approximation
Light and Matter [Sakurai ch1+2, L ch20+21]
- review of E&M, gauge invariance, Coulomb gauge, photons, spontaneous emission, black body radiation, Kramers-Heisenberg formula, Thomson, Compton, Rayleigh scattering, photo-electric effect
Spin Systems [class notes]
- spin, para- and ferromagnetism, Heisenberg model, Ising model, spin waves, momentum space, Hubbard model, t-j model, critical phenonena, renormalization group, universality.
Bosonic Systems [MYS ch 8]
- phonons, liquid ⁴He, density fluctuations, Bogoliubov model, rotons, zero sound

If time permits we will touch on superconductivity, nuclear matter, and the finite temperature formalism.

Problem Sets