After successful completion of the course, students are able to

• compute partition functions of free scalar, fermionic and gauge field theories (path integral quantization);
• calculate their thermodynamic properties and propagators (Matsubara formalism, real-time formalism);
• apply Feynman rules to thermal field theories (for loop expansions) and re-organize perturbation theory using IR resummation and 1PI formalism;
• compute self-energies at 1-loop level using hard thermal loop (HTL) approximations, concrete example: photon polarization tensor and resulting dispersion relations;
• write path integrals of non-thermal field theories (Schwinger-Keldysh time contour);
• derive the classical-statistical approximation of the full quantum field theory;
• use 2PI formalism to derive exact field equations for propagators and to employ alternative truncations schemes

1. Introduction: Statistical quantum mechanics, relativistic thermodynamics, propagators of many-body systems, perturbation theory, Matsubara formalism, Schwinger-Keldysh formalism, scalar, fermionic and gauge theories at finite temperature; 2. Applications: 2.1. Collective phenomena in a relativistic plasma: quasi-particle spectrum in QED and Quark-Gluon plasma, improvements of perturbation theory; 2.2. Phase transitions: spontaneous symmetry breaking and symmetry restoration at high temperature, effective potential; 2.3. non-thermal quantum field theory, classical-statistical approximation, 2PI formalism and exact evolution equations.

• blackboard lecture;
  
• possibly presentation of slides / images;
• voluntary exercises to deepen the understanding of the teaching material.

The lecture will mostly follow the lecture notes by A. Schmitt and A. Rebhan. Additionally, lecture notes by M. Laine  and A. Vuorinen are very useful to improve one's understanding of thermal field theory. The part covering non-thermal field theory will be based on lecture notes by J. Berges.

Links to the scripts and more information and announcements will be available at http://www.itp.tuwien.ac.at/Homepage_Kirill_Boguslavski.

By arrangement, written exam at the end of the semester or oral exam.

Basic knowledge of quantum field theory recommended but not mandatory