THERMAL FIELD THEORY (FYSH520 X PTS), FALL 2025

General

Lecturer:
Kimmo Kainulainen
FL216
Lectures 28 h:
Tue and Wed 14.15-16.00
Variable locations, check every time
Course time (approx):
7.9.-1.12

Grading
lecturer
FL216
Excercises 28 h:
Wed 12.15-14.00 
Changing location
EXAM = Individual Final Projects
-8.12 / Negociable
 

Any time. It is possible to get the course credits also outside JyU.

Course description

Course covers basic topics in the finite temperature field theory. We start from quantum statistical physics for bosonic and fermionic systems. Then we quantize the free bosonic, fermionic and gauge-fields and derive their thermodynamics using path integral methods and imaginary time formalism (ITF). Phenomena studied include Bose condensation and black body radiation. We move to interacting field theories again starting from Bosonic systems. We study renormalization in finite temperature and compute the pressure up leading nontrivial order, and introduce resummation techniques to overcome infrared singularities. We study the effective action and the effective potential and its applications in first order phase transitions, including evaluation of the transition strength, thermodynamical quantitites and bubble nucleation rate and growth. We then introduce the real-time formulation (RTF) of the finite temperature field theory. We show the necessity of the two time-histories and intdoduce the the concept of the Keldysh (and more general) complex-time path. We then derive the RTF 2x2 Feynman rules for scalar, fermion and gauge fields and derive connections between the different correlation functions appearing in the RTF and ITF formulations. We then introduce the concept of quasiparticles in a thermal plasma and derive the dispersion relations for the particle- and hole excitations for fermions and plasmon dispersion relations for the gauge fields.

Source literature

J. Kapusta
Finite Temperature Thermal Field Theory
M. LeBellac
Thermal Field Theory
M. Laine and A. Vuorinen
Basics of Thermal Tield Theory
 

Lecture notes

The lectrure notes in latex are here and the handwritten notes can be found here: part 1, part 2 and part 3. The Dolan and Jackiw article is here.

Excercises

Ex. 1-2 Ex. 3-4 Ex. 5-6 Ex. 7-8 Ex. 9-10 Ex. 11-12

Final projects

Some suggestions for the final project problems are here. (To be updated.)  


Kimmo Kainulainen
Last edited: 15 September 2025