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M. Gal:
"Soliton Approximation in Lattice Quantum Chromodynamics";
Supervisor: M. Faber; Atominstitut, 2012; final examination: 2012-06-06.

Quantum chromodynamics is the accepted quantum field theory of the strong interaction between quarks and gluons. One of the most interesting questions of QCD is the confinement of quarks.
Confinement emerges from excitations of the QCD vacuum.
Three excitations have been proposed to lead to quark-confinement, namely instantons, magnetic monopoles and vortices. Only two of them can reproduce the experimental measured string tension, monopoles in the dual superconductor model and center vortices in the vortex model.

In lattice QCD both objects, monopoles and vortices, are detected by fixing a gauge. Monopoles as sources of magnetic flux and vortices as quantized magnetic flux tubes should rather be physical objects. It would be desirable to find them as gauge invariant objects.
Motivated by the idea that magnetic monopoles in $U(1)$ gauge theory are point-like gauge invariant objects and $U(1)$ theory can be extended to an $SU(2)$ scalar field theory with extended monopoles we try to approximate $SU(2)$-QCD by an $SU(2)$ scalar field. From this scalar field an $SU(2)$ vector field can be derived. We aim to check how far this derived $SU(2)$ vector field can reproduce the properties of the original $SU(2)$ gauge field of QCD.

Chapters 1 and 2 give a brief introduction to the basics of lattice calculations and QCD. Chapters 3 and 4 will introduce the model of topological fermions and its simulation. In chapter 5 the soliton approximation algorithm is presented in detail. In order to search for structures within the gauge-field the algorithm was further modified to scan parts of the lattice. In chapter 6 we discuss the properties of the soliton approximation with the usage of different gauges and its results. We take a closer look on the link and plaquette distributions, Wilson loops and Creutz ratios.

In the last chapter we present a new approach to investigate the structure of the $SU(2)$ gauge-field.

http://publik.tuwien.ac.at/files/PubDat_227048.pdf