Thermal Field Theory
Time:
Wed 14-16, Fri 10-12, starting 21.04.2004.
Place:
D6-135.
Background:
Quantum field theory / statistical physics.
Literature:
* J.Kapusta, Finite-Temperature Field Theory.
* M. Le Bellac, Thermal Field Theory.
Schedule:
Contents.
21.04.:
Quantum mechanics. Partition function Z. Path integral for Z.
(p.1-4)
23.04.:
Evaluation of Z for harmonic oscillator.
(p.5-8)
Exercise 1 & solution.
(p.9-11)
28.04.:
Scalar field theory. Fourier representation for Z.
(p.12-14)
30.04.:
Evaluation of thermal sums.
(p.15-18)
Exercise 2 & solution.
(p.19-21)
05.05.:
Small-T expansion. Dimensional regularization.
(p.22-25)
07.05.:
Large-T expansion. Gamma and zeta functions.
(p.26-29)
Exercise 3 & solution.
(p.30-32)
12.05.:
Interactions. Weak coupling expansion. Wick's theorem.
(p.33-35)
14.05.:
Propagator. Z naively to order lambda & lambda**2.
(p.36-39)
Exercise 4 & solution.
(p.40-42)
19.05.:
UV renormalisation. Z properly to order lambda.
(p.43-46)
21.05.:
IR resummation. Z properly to order lambda**3/2.
(p.47-49)
Exercise 5 & solution.
(p.50-52)
26.05.:
Path integral for Z of fermionic harmonic oscillator.
(p.53-56)
28.05.:
The Dirac field at finite T. Fermionic sums.
(p.57-60)
Exercise 6 & solution.
(p.61-63)
02.06.:
Gauge fields; QCD, QED. Path integral for Z.
(p.64-67)
04.06.:
Gauge fixing, ghosts. Feynman rules.
(p.68-70)
Exercise 7 & solution.
(p.71-73)
09.06.:
Thermal masses, electric vs magnetic.
(p.74-77)
11.06.:
Z to order g**3.
(p.78-81)
Exercise 8 & solution.
(p.82-84)
16.06.: No lecture.
18.06.: No lecture.
23.06.:
The IR problem at finite T. Low-energy effective field theories.
(p.85-89)
25.06.:
Dimensional reduction of QCD.
(p.90-92)
Exercise 9 & solution.
(p.93-95)
30.06.:
Finite density. Complex scalar field.
(p.96-98)
02.07.:
Effective potential; BEC. Dirac fermion at finite density.
(p.99-102)
Exercise 10 & solution.
(p.103-104)
07.07.:
Real-time observables.
(p.105-108)
Appendix: basic relations for fermions.
09.07.:
A sample computation.
(p.109-112)
Exercise 11 & solution.
(p.113-114)
14.07.:
Hard Thermal Loops.
(p.115-119)
16.07.:
Applications. Cosmological background.
(p.122-125)
Exercise 12 & solution.
(p.120-121)
21.07.:
Thermal phase transitions.
(p.126-129)
23.07.:
Bubble nucleation rate.
(p.130-133)
Exercise 13 & solution.
(p.134-135)
28.07.:
Particle production rates.
(p.136-139)
30.07.: No lecture.
Update:
New version.