Universität Leipzig

Quantum Field Theory on Curved Spacetimes
Summer Term 2016




Prof. R. Verch
ITP, Universität Leipzig
Brüderstr. 14-16
Phone: +49 341 97 32423

Dr. T.-P. Hack
ITP, Universität Leipzig
Brüderstr. 14-16
Phone: +49 341 97 32444

Webpage: Rainer Verch


Problem Sheet 7 published, see below.

From 13 June, please switch to the updated copy of this page at this URL to see the current problem sheets and announcements.

And here are the slides.pdf of the lectures of the first week.

Termine/Dates (and Locations)

Wed 11:15-12:45, IPT, Brüderstr. 16, Room 114 (1st floor)
Thu 13:30-15:00, ITP, Brüderstr. 16, Room 114 (1st floor)

Übungen/Exercise Class
Mon 09:15-10:45 , ITP, Brüderstr. 16, Room 114 (starts 11 Apr.)


The lecture will start with Quantum Field Theory (QFT) on Minkowski spacetime and discuss the relevant concepts and results. The second half will give an introduction to QFT on curved spacetimes and applications.

Topics include:
  • quantum fields and particles
  • the mathematical framework of QFT
  • spin and statistics, PCT
  • models of quantum fields
  • concepts of locality and covariance
  • Hawking effect
  • semi-classical gravity
  • QFT and cosmological inflation

  • Empfehlenswerte Literatur/Recommended Literature:

  • E.M. Henley, W. Thirring: Elementary Quantum Field Theory, McGraw-Hill, 1962
  • R.F. Streater, A.S. Wightman: PCT, Spin and Statistics, and All That, Princeton University Press, 1980 (original edition: W.A. Benjamin, 1964)
  • R. Haag: Local Quantum Physics, Springer-Verlag, 1996
  • O. Steinmann: Perturbative Quantum Electrodynamics and Axiomatic Field Theory, Springer-Verlag, 2000
  • R.M. Wald, Quantum Field Theory in Curved Spacetimes and Black Hole Thermodynamics, University of Chicago Press, 1994
  • R. Brunetti, C. Dappiaggi, K. Fredenhagen, J. Yngvason, Editors: Advances in Algebraic Quantum Field Theory, Springer-Verlag, 2015
  • C. Bär, N. Ginoux, F. Pfäffle: Wave Equations on Lorentzian Manifolds and Quantization. EMS, 2007
  • T.-P. Hack: Cosmological Applications of Algebraic Quantum Field Theory in Curved Spacetimes, Springer, 2016
  • G.F.R. Ellis, R. Maartens and M.A.H. MacCallum: Relativistic Cosmology, Cambridge University Press, 2012
  • N. Straumann, ``From primordial quantum fluctuations to the anisotropies of the cosmic microwave background radiation,'' Annalen Phys. 15 (2006) 701 [arXiv:hep-ph/0505249]

  • Additional Material

    Mathematical (and other) aid kits:
  • M. Reed, B. Simon: Methods of Modern Mathematical Physics, Vols. 1 & 2, Academic Press, 1980 (or more recent editions)
  • B. Thaller: The Dirac Equation, Springer-Verlag, 1992
  • K. Sundermeyer: Symmetries in Fundamental Physics, Springer-Verlag, 2014
  • V. Moretti: Spectral Theory and Quantum Mechanics, Springer-Verlag, 2013
  • R.U. Sexl, H.K. Urbantke: Relativity, Groups, Particles, Springer-Verlag, 2001

  • Übungsaufgaben/Exercise Sheets

  • Sheet 1
  • Sheet 2
  • Sheet 3
  • Sheet 4
  • Sheet 5
  • Sheet 6
  • Sheet 7