linkCurriculum vitae

TPI uni-jena

Dr. habil. Georg Bergner
Theoretisch-Physikalisches Institut
Friedrich-Schiller-Universität Jena
Max-Wien-Platz 1
D-07743 Jena
Tel.: +49-3641-947139
Email: georg.bergner
Room: Abb 202


Lecture: Lattice Quantum Field Theory: Principles and Applications


Tuesday from February 23 until April 26, 14:15-16:00, room 119
No lecture on April 22 and 26


The numerical simulations on a space-time lattice are a well-established method for the investigation of strongly coupled quantum field theories. Especially our knowledge about Quantum Chromodynamics (QCD) relies to a large extend on this numerical approach. It is extremely important to relate the bound state spectrum and important mechanisms like confinement to the fundamental theory. This course offers a brief review about the methods of numerical lattice simulations. I will start with a summary of the foundations based on the path integral formulation and statistical physics. Then the techniques for the representation of a quantum field theory with scalar, gauge, and fermion fields on the lattice will be reviewed. In the end of the course I will focus on the applications in QCD and Yang-Mills theories concerning the bound state spectrum and thermodynamics. The general aim of the course is to provide an overview about the prospects and challenges of the method for non-experts in the field.

Preliminary outline

  • History, Basics, Motivation
  • Scalar and gauge fields on the lattice
  • Fermions on the lattice
  • Lattice QCD
  • Weak, strong, continuum, and infinite volume limit
  • Bound states
  • Thermodynamics
  • New applications and outlook


  • Montvay, M√ľnster, "Quantum Fields on a Lattice", Cambridge University Press (1994)
  • Smit, "Introduction to Quantum Field on a Lattice", Cambridge Lecture Notes in Physics (2002)
  • Rothe, "Lattice Gauge Theories An Introduction" World Scientific (2005)
  • DeGrand, DeTar, "Lattice Methods For Quantum Chromodynamics", World Scientific (2006)
    Focused on QCD, not very detailed
  • Gattringer, Lang, "Quantum Chromodynamics on the Lattice", Springer (2010)
    most modern reference; some focus on algorithms
  • Wipf, "Statistical Approach to Quantum Field Theory", Springer (2013)
    alternative approach
  • Creutz, "Quarks, gluons, and lattices", Cambridge University Press (1985)
    not quite up to date
  • Rebbi, "Lattice gauge theories and Monte Carlo simulations", World Scientific (1983)
    collection of historical works