Computational Methods in Quantum Field Theory

Abstract

After a brief introduction to the statistical description of data, these lecture notes focus on quantum field theories as they emerge from lattice models in the critical limit. For the simulation of these lattice models, Markov chain Monte-Carlo methods are widely used. We discuss the heat bath and, more modern, cluster algorithms. The Ising model is used as a concrete illustration of important concepts such as correspondence between a theory of branes and quantum field theory or the duality map between strong and weak couplings. The notes then discuss the inclusion of gauge symmetries in lattice models and, in particular, the continuum limit in which quantum Yang-Mills theories arise.

50 pages, 16 figures, notes based on a lecture presented at the XIX Physics Graduate Days at the University of Heidelberg, 8th - 12th October 2007

References in corpus (6)

• Scaling of the distribution of fluctuations of financial market indices
• A construction of lattice chiral gauge theories
• A practical implementation of the Overlap-Dirac operator
• A study of chiral symmetry in quenched QCD using the Overlap-Dirac operator
• Overlap Quark Propagator in Landau Gauge
• Improved actions and asymptotic scaling in lattice Yang-Mills theory