Eichtheorien bei endlicher Temperatur
Gauge Theories at finite temperature

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

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.

Quantenmechanik I + II, Thermodynamik, Grundlagen der Quantenfeldtheorie, wünschenswert wären ebenfalls Grundkenntnisse über Feldtheorie bei endlicher Temperatur.

Einige störungstheoretische Methoden werden in der Vorlesung entwickelt.

In einer mündlichen Prüfung wird das Erreichen der Lernergebnisse durch Verständnisfragen und Beispielaufgaben bewertet.

Die Prüfung kann in Übereinstimmung mit §12 (8) APSO auch schriftlich abgehalten werden, in diesem Fall ist der Richtwert für die Prüfungsdauer 60 Minuten.