Lecture: Lattice Quantum Field Theory: Principles and Applications

Dates

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

Abstract

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

Literature

• Montvay, Münster, "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