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Gauge Theories at finite temperature

Module PH2121

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

PH2121 is a semester module in English language at Master’s level which is offered in summer semester.

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
150 h 75 h 5 CP

Responsible coordinator of the module PH2121 is Norbert Kaiser.

Content, Learning Outcome and Preconditions


Understanding gauge theories at finite temperature is necessary for the description of many phenomena under extreme conditions. Examples include a hot plasma of electrons and protons in a laser experiment or the quark-gluon plasma which is created in heavy-ion collisions, e.g. at the Large Hadron Collider at CERN.

Since gauge theories describe the fundamental interactions, one needs a formalism to address finite-temperature problems with these theories. We will introduce the basics of these methods.

Specifically, we will treat Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD) at finite temperature. Topics will include:
- Gauge fixing in gauge theories
- Quantization of gauge theories
- Perturbative methods
- Finite-temperature formalism for gauge theories
- Screening
- Hard thermal loop resummations
- Strong coupling expansion in QCD and the Polyakov loop
- Infrared singularities at finite temperature (Linde problem)
- Renormalization Group methods

Learning Outcome

Students will acquire the ability to solve problems in gauge theories at finite temperature. They will learn about the specific problems that arise in this context and learn about the methods that have been developed to address them. They will gain an overview over these methods and the connections to current research topics. At the end of the course, they will be able to assess such problems and place them in the context of current research efforts.

To gain proficiency with the calculational methods, it is imperative to work on the homework problems which will be provided. Students will be able to master perturbative calculations at finite temperature for standard problems.


Quantum Mechanics I + II, Thermodynamics, Basics of Quantum Field Theory, some knowledge of Finite Temperature Field Theory would be desirable, but is not absolutely necessary.

Some perturbative methods will be presented in the lecture.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VU 4 Gauge Theories at finite temperature singular or moved dates
and dates in groups

Learning and Teaching Methods

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Module Exam

Description of exams and course work

In an oral exam the learning outcome is tested using comprehension questions and sample problems.

In accordance with §12 (8) APSO the exam can be done as a written test. In this case the time duration is 60 minutes.

Exam Repetition

The exam may be repeated at the end of the semester. There is a possibility to take the exam in the following semester.

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