Lecture: Computational Methods for Particle Physics (WS 2021/22)
Due to COVID-19 restrictions: online course based on Zoom and LearnWeb.
Programming course and exercises. Introduction to Monte-Carlo methods up to simulations of Yang-Mills-Theories.
Ising model simulations.
Ising model and related theories, low and high temperature expansions, simulation algorithms
Gauge principle and gauge theories in the continuum, formulation of pure gauge theory on the lattice.
Simulation algorithm for SU(2) pure gauge theory, implementation of SU(2) metropolis algorithm
Material (see LearnWeb of WWU)
Simple solution in Fortran
Simple solution in C
In order to compile the exectuables, put all files in a common directory and call "make".
Simple solution in Python
Faster solution in Python3 using Numba
Parameter file faster version
This exercise is to write a simple metropolis update code for SU(2) pure gauge theory. In order to simplify the task, several routines for
handling configurations, links, matrices, and random numbers are already provided.
C++ and Fortran code as a staring point for the exercise of SU(2) pure gauge lattice simulations.
For the C++ program you have to call "make Eigen" first. Additional dependence: Boost library (please install on your system).
Simple example solution SU(2) pure gauge lattice simulations (C++ and Fortran).
Literature / References
Many different examples for Ising model simulations in various programming languages are avaiable online.
Wipf, "Statistical Approach to Quantum Field Theory", Springer (2013)
The following books contain further information on simulations of pure gauge theory on the lattice:
Gattringer, Lang, "Quantum Chromodynamics on the Lattice", Springer (2010)
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)