Introduction to Quantum Gauge Theories on Supercomputers

Who: Martin Rasmus Lundquist Hansen
When: Wednesday, August 1, 2012

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Gauge theories currently dominates our description of elementary particles and their interactions. Starting from the theory of electrodynamics (the simplest of the gauge theories) I will introduce abelian and non-abelian gauge theories. As a precursor I will discuss classical field theory and the Lagrangian formulation. I will in particular introduce Noether’s theorem and show the important connection between continuous symmetries of the Lagrangian and conservation laws. When introducing gauge theories we discover why the existence of gauge fields and gauge invariance is a necessity and my work will eventually lead to non-abelian gauge theories and the famous Yang-Mills Lagrangian. Computation of quantities associated with gauge theories are in most cases difficult to perform analytically. This leads to the introduction of the path integral formulation as a modern way to quantise quantum gauge theories.

When all the prerequisites are in place I will introduce numerical techniques to simulate quantum gauge theories via a discretised four-dimensional spacetime lattice. The lattice formulation will enable me to perform simulations of a pure SU(2) gauge theory using the path integral formulation and the heat-bath algorithm. The simulation will allow me to extract the string tension (of the static quark-antiquark potential) and analyse properties such as confinement and asymptotic freedom. These results will be interpreted in connection with the theory of the strong nuclear interaction, quantum chromodynamics.

The bachelor project is available as PDF.