Computational Methods in Quantum Field Theory
Abstract
Description
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
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