Thermal Field Theory
Related summer school lectures, from 2010, in
slide format
.
Lecturer:
Mikko Laine
Time:
Tue 10-12, Thu 12-14, starting 16.10.2007.
Place:
D6-135.
Background:
Quantum field theory / statistical physics.
Literature:
* C. Gale and J.I. Kapusta, Finite-Temperature Field Theory.
* M. Le Bellac, Thermal Field Theory.
Schedule:
Contents.
16.10.:
Quantum mechanics. Partition function Z. Path integral for Z.
18.10.: No lecture.
23.10.:
Evaluation of Z for harmonic oscillator. Exercise 1 & solution.
25.10.:
Free scalar fields. Path integral for Z. Fourier representation.
30.10.:
Evaluation of thermal sums. Exercise 2 & solution. Low-T expansion.
01.11.: No lecture.
06.11.:
High-T expansion. Gamma and zeta functions. Exercise 3 & solution.
08.11.:
Interactions. Weak coupling expansion. Wick theorem. Propagator.
13.11.:
Z naively to order lambda & lambda**2. Exercise 4 & solution.
15.11.:
UV renormalisation. Z properly to order lambda.
20.11.:
IR resummation. Z properly to order lambda**3/2. Exercise 5 & solution.
22.11.:
Path integral for Z of fermionic harmonic oscillator.
27.11.:
The Dirac field at finite T. Fermionic sums. Exercise 6 & solution.
29.11.:
Gauge fields. Path integral for Z.
04.12.: No lecture.
06.12.:
Gauge fixing, ghosts. Feynman rules. Exercise 7 & solution.
11.12.:
Thermal gluon mass.
13.12.:
Z to order g**3. Exercise 8 & solution.
18.12.:
The IR problem at finite T. Low-energy effective field theories.
20.12.:
Dimensional reduction of QCD. Exercise 9 & solution.
08.01.:
Finite density. Complex scalar field. Effective potential; BEC.
10.01.:
Dirac fermion. Chemical potentials and gauge symmetry. Exercise 10 & solution.
15.01.:
Real-time observables. Different Green's functions.
17.01.:
From Euclidean correlator to spectral function. Exercise 11 & solution.
22.01.:
Hard Thermal Loops.
24.01.:
Relation to classical kinetic theory. Exercise 12 & solution.
29.01.:
Thermal phase transitions.
31.01.:
Bubble nucleation rate. Exercise 13 & solution.
Particle production rate.
05.02.:
Dark matter abundance in cosmology.
07.02.:
Transport coefficients.
Further reading.
As a reference:
Old version.