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FSI3330 Thermal Field Theory 7.5 credits

The course will provide basic understanding and some applications of relativistic thermal quantum field theory. Statistical methods are nowadays widely used in condensed matter physics, plasma physics, collider physics (hadron colliders), and cosmology. This course will focus on the basic concepts of relativistic statistical systems and their applications to cosmology. The course starts with a brief review of statistical physics and quantum field theory (QFT). Even though basic knowledge in both fields is required, a significant part of the lectures is used to solidify fundamental aspects of QFT that appear in statistical systems in similar fashion as in vacuum. In addition, some concepts that are usually not covered in a first course of QFT are discussed and applied to thermal systems, e.g. fermionic path integrals, Goldstone's theorem, and Ward identities. The second part of the course addresses more recent developments in thermal field theory as e.g. resummation techniques, dynamical screening, and hard thermal loops. In the third part, applications to cosmology are discussed. This could include some topics of the following list: Spontaneous symmetry breaking and restoration, phase transitions and inflation, transport equations and baryogenesis.

Course offering missing for current semester as well as for previous and coming semesters
Headings with content from the Course syllabus FSI3330 (Spring 2019–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

Part I:

  • Introduction. General concepts of statistical physics and quantum field theory
  • Quantization of the bosonic field at finite temperature; Matsubara frequencies; Feynman rules at finite temperature
  • Quantization of the fermionic field at finite temperature; fermionic path integrals and coherent state formalism
  • Quantization of the gauge fields at finite temperature; ghosts and blackbody radiation; static screening
  • Renormalization and infrared problems
  • Collective excitations in a plasma
  • Equivalence of real-time and imaginary-time formalism

Part II:

  • Linear response theory
  • Resummation and effective actions; Daisy diagrams
  • Hard thermal loop expansion
  • Dynamical screening

Part III:

  • Spontaneous symmetry breaking and restoration
  • Phase transitions and inflation
  • Transport equations and baryogenesis; Kadanoff-Baym equations in Wigner space

Intended learning outcomes

Upon passing the course the student should:

  • Be able to recount how a finite temperature and density background affects field theoretical computations.
  • Treat bosonic and fermionic systems and quantization within thermal field theory.
  • Be able to use thermal field theory to describe spontaneous symmetry breaking at finite temperature.

Course disposition

Lecture I: Introduction. Canonical ensembles in statistical physics. Path integral formulation of quantum mechanics.

Lecture II: Imaginary time formalism of bosonic systems.

Supplement I: Regulariziation and renormalization in QFT.

Lecture III: Real time formalism of bosonic systems.

Lecture IV: Fermionic systems in TFT.

Lecture V: Quantization of gauge fields in QFT and TFT.

Lecture VI: Seminars.

Lecture VII: Spontaneous symmetry breaking at finite temperature. Seminar.

Supplement II: Non-abelian gauge fields.

Lecture VIII: Seminar.

Lecture IX: Seminar. Quantum Boltzmann equations from the real time formalism.

Discussion of the problem set.

Literature and preparations

Specific prerequisites

The course is mainly intended to graduate students with interest in theoretical physics and cosmology. Basic knowledge in statistical mechanics and quantum field theory are prerequesites.

Recommended prerequisites

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  • M. Le Bellac, Thermal field theory, Cambridge University Press, 1996
  • J. I. Kapusta, Finite-temperature field theory, Cambridge University Press, 1989

Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

P, F


  • INL1 - Assignment, 7,5 hp, betygsskala: P, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Other requirements for final grade

Hand in assignments.

Opportunity to complete the requirements via supplementary examination

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Opportunity to raise an approved grade via renewed examination

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Profile picture Tommy Ohlsson

Ethical approach

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course web

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Offered by


Main field of study

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Education cycle

Third cycle

Add-on studies

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Mattias Blennow (

Postgraduate course

Postgraduate courses at SCI/Physics