**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:

- J.P. Blaizot and G. Ripka,
*Quantum Theory of Finite Systems* - P. Ring and P. Schuck,
*Nuclear Many-Body Problem* - J. Negele and H. Orland,
*Quantum Many Particle Systems*

**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
^{4}He, density fluctuations, Bogoliubov model, rotons, zero sound

- phonons, liquid

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

**Problem Sets**

- set 1 [pdf] due Sept 5
- set 2 [pdf] due Sept 17
- set 3 [pdf] due Oct 6
- set 4 [pdf] due Oct 15
- set 5 [pdf] due Oct 27
- set 6 [pdf] due Oct 29
- set 7 [pdf] due Nov 17
- set 8 [pdf] due Dec 12
- set 9 [pdf] due Dec 12