# 136.086 Thermal field theory This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2024S 2023S 2022S 2021S

2024S, VO, 2.0h, 3.0EC

## Properties

• Semester hours: 2.0
• Credits: 3.0
• Type: VO Lecture
• Format: Hybrid

## Learning outcomes

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.

## Subject of course

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)
6. Specialized topics if time allows

## Teaching methods

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

## Mode of examination

Oral

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.)

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.

• 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.

Lecture:

• Beginning of the course: 10.04.2024
• Wednesday, at 12:00 - 14:00

## Course dates

DayTimeDateLocationDescription
Wed12:00 - 14:0006.03.2024 - 26.06.2024Sem.R. DB gelb 10 Thermische Quantenfeldtheorie
Thermal field theory - Single appointments
DayDateTimeLocationDescription
Wed06.03.202412:00 - 14:00Sem.R. DB gelb 10 Thermische Quantenfeldtheorie
Wed13.03.202412:00 - 14:00Sem.R. DB gelb 10 Thermische Quantenfeldtheorie
Wed20.03.202412:00 - 14:00Sem.R. DB gelb 10 Thermische Quantenfeldtheorie
Wed10.04.202412:00 - 14:00Sem.R. DB gelb 10 Thermische Quantenfeldtheorie
Wed17.04.202412:00 - 14:00Sem.R. DB gelb 10 Thermische Quantenfeldtheorie
Wed24.04.202412:00 - 14:00Sem.R. DB gelb 10 Thermische Quantenfeldtheorie
Wed08.05.202412:00 - 14:00Sem.R. DB gelb 10 Thermische Quantenfeldtheorie
Wed15.05.202412:00 - 14:00Sem.R. DB gelb 10 Thermische Quantenfeldtheorie
Wed22.05.202412:00 - 14:00Sem.R. DB gelb 10 Thermische Quantenfeldtheorie
Wed29.05.202412:00 - 14:00Sem.R. DB gelb 10 Thermische Quantenfeldtheorie
Wed05.06.202412:00 - 14:00Sem.R. DB gelb 10 Thermische Quantenfeldtheorie
Wed12.06.202412:00 - 14:00Sem.R. DB gelb 10 Thermische Quantenfeldtheorie
Wed19.06.202412:00 - 14:00Sem.R. DB gelb 10 Thermische Quantenfeldtheorie
Wed26.06.202412:00 - 14:00Sem.R. DB gelb 10 Thermische Quantenfeldtheorie

## Examination modalities

Oral exam by arrangement at the end of the semester.

## Course registration

Begin End Deregistration end
14.02.2024 02:00

### Registration modalities

The registration takes place in TISS. A certificate is only issued if the examination has been completed and passed.

## Curricula

Study CodeObligationSemesterPrecon.Info
066 461 Technical Physics Mandatory elective

## Literature

No lecture notes are available.

## Previous knowledge

Electrodynamics I and Quantum Mechanics I.

Electrodynamics II, Statistical Physics I and previous knowledge of quantum field theory are helpful but not mandatory since all necessary quantum field theoretical concepts will be introduced during the course.

English