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);
• apply Feynman rules to thermal field theories (for loop expansions) and re-organize perturbation theory using IR resummation and 1PI formalism;
• write path integrals of non-thermal field theories (Schwinger-Keldysh time contour);
• apply real-time methods (real-time formalism, classical-statistical theory, 2PI formalism) to compute observables;
• calculate self-energies at 1-loop level using hard thermal loop (HTL) approximations, concrete example: photon polarization tensor and resulting dispersion relations.

1. Introduction:
   (applications, statistical quantum mechanics, relativistic thermodynamics)
2. Path integrals, Z, W:
   (generating functionals, 1PI effective action)
3. Matter and interactions:
   (scalar field theory, Matsubara formalism, symmetry restoration, perturbation theory, infrared resummations, fermion fields)
4. Real-time and non-equilibrium quantum field theory:
   (Schwinger-Keldysh path integral, propagators, real-time formalism, methods: real-time perturbation theory, classical-statistical theory, Kadanoff-Baym / 2PI equations)
5. Gauge fields, hard-thermal loop theory (HTL):
   (Lagrangians of QED and QCD, path integral quantization, propagators, HTL self-energies, collective excitations)

• blackboard lecture / Zoom;
  
• voluntary exercises to deepen the understanding of the teaching material.

This is an introductory course to thermal and non-thermal quantum field theory.

Registration modalities: Registration takes place in TISS. (Registration is without commitment, and does not result in an automatic issuing of a certificate.)

More information, announcements and the links to the Zoom lectures and to my (hand-written) lecture notes will be available on TUWEL.

The lecture will partially follow the lecture notes by A. Schmitt and A. Rebhan. Additionally, lecture notes by M. Laine and A. Vuorinen and the book by M. Peskin and D. Schroeder are very useful to improve one's understanding of (thermal) quantum field theory. The part covering real-time field theory will be based on the review by J. Ghiglieri, A. Kurkela, M. Strickland and A. Vuorinen and on the lecture notes by J. Berges.

Links to the scripts:

• A. Schmitt (revised by A. Rebhan), Thermal field theory (script also linked on TUWEL), the lecture will cover most of the topics of this manuscript but in a different order (and some parts will be dropped);
• M. Laine and A. Vuorinen, Basics of Thermal Field Theory, more detailed lecture notes, some topics of the lecture will follow this work;
• M. Peskin and D. Schroeder, An Introduction to Quantum Field Theory, for functional methods (path integrals, Z, W, 1PI effective action) see Chapters 9 and 11;
• J. Ghiglieri, A. Kurkela, M. Strickland and A. Vuorinen, Perturbative Thermal QCD: Formalism and Applications, topics like the real-time and HTL formalisms are based on Secs. 2 - 4 of this review;
• J. Berges, Introduction to Nonequilibrium Quantum Field Theory, covers topics on 2PI and on nonequilibrium field theory.

Oral exam by arrangement at the end of the semester.

Basic knowledge of quantum field theory recommended but not mandatory