ECT Doctoral Program Week 1

Mo 10:00-11:00 11:30-12:30

Tu 10:00-11:00 11:30-12:30

Seminar 1: Dimity Kobyakov, Collective Modes in the Inner Crust of Neutron Stars

Tu 14:30-15:00

We 10:00-11:00 11:30-12:30

Discussion Session

We 14:00-15:00

Lecture 4: QCD at finite density

Th 10:00-11:00 11:30-12:30

Seminar 2:

Th 14:00-15:00

Lecture 5: Non-equilibrium QCD

Fr 10:00-11:00 11:30-12:30

Discusion Session

Fr 14:00-15:00

Other resources:

1) A set of lecture notes on the phase structure of QCD.

2) Lecture notes on many body physics.

About confinement and chiral symmetry breaking:

Not much is known in terms of rigorous or systematic approaches

to these phenomena in QCD. Here are some suggested activities

and resources.

1) Write a pure gauge lattice QCD code (for simplicity, consider SU(2))

and measure the heavy quark potential using Wilson loops. See the

nice old book by Creutz, or the more recent book by Gattringer. This

is not supercomputing, your laptop will do the trick!

2) The simplest analytically tractable theory that exhibits confinement

in a non-trivial way is the Polyakov model, see the nice discussion

in Shifman's book.

3) My own most recent attempt is described in this talk.

4) A microscopic picture of chiral symmetry breaking is provided

by the instanton model, see Sect IV.E. of this review (approximately

self-contained).

Simple exercises in many-body physics:

1) Solve the 2-body Schroedinger equation for a contact interaction using

diagrammatic methods (see Sect.1 of the many-body review cited above).

2) For a dilute, weakly interacting Fermi gas compute the O((k_Fa)^0) and

O((k_Fa)) contributions to the energy per particle.

3) Use the Hubbard-Stratonovich trick to rewrite the four-fermion contact

interaction as a 2-fermion-difermion coupling.

4) Follow the steps described in the many-body lectures to compute the

BCS gap in the weak coupling limit (|k_Fa}<1).