Title: Topological objects and chiral symmetry breaking in QCD
Language: English
Authors: Schweigler, Thomas
Qualification level: Diploma
Keywords: QCD; topologische Objekte; spontane chirale Symmetriebrechung; sphärischer Vortex
QCD; topological objects; spontaneous chiral symmetry breaking; spherical vortex
Advisor: Faber, Manfried
Assisting Advisor: Höllwieser, Roman
Issue Date: 2012
Number of Pages: 89
Qualification level: Diploma
In this master thesis, topological objects in SU(2) gauge theory are investigated. Besides investigating the objects in general, I also tried to find out more about their importance for spontaneous chiral symmetry breaking.
The lattice gauge object, whose properties have been mainly investigated, is the spherical vortex. The spherical vortex seems to be some sort of squeezed instanton. In this document, a very detailed investigation of the spherical vortex is performed. The investigation takes place partly in the continuum and partly on the lattice.
In previous work, only spherical vortices with temporal extent of one lattice unit have been investigated. For such objects, one gets vanishing topological charge but nonvanishing index=1 of the Dirac operator. In this document, it is shown that this discrepancy is simply a discretization effect. For growing temporal extent of the vortex, the lattice topological charge approaches 1 and the index theorem is fulfilled again. Moreover, the action and topological charge density of the spherical vortex have been calculated analytically in the continuum.
The spatial and temporal localization of the zeromode(s) for the spherical vortex have been investigated.
Another investigation concerned the lowest nonzero eigenvalues of the Dirac operator for the spherical vortex. It was demonstrated that, for the vortex getting smaller and smaller, these eigenvalues approach the eigenvalues of the free Dirac operator. The zeromode occurs no matter how small the vortex becomes. Moreover, it was checked for the lowest non-zero-modes, if the self-dual/anti-self-dual gauge field contributions attract the negative/positive chiral components of the eigenmodes. The results for the localization of the scalar and the chiral density are in agreement with this picture. The same investigation was also done for the lowest non-zero-modes for the instanton. It is interesting to see, that in case of the the instanton (consisting only of self-dual field contributions) only negative chiral components are attracted by the object, in case of the spherical vortex (consisting of both self-dual and anti-self-dual contributions) also positive chiral components are attracted by the object.
Last but not least, the interaction between a spherical vortex and a spherical "antivortex" (object with topological charge -1) has been investigated. The transformation of the two would-be zeromodes into two near-zero modes was demonstrated.
URI: https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:1-54538
Library ID: AC07814235
Organisation: E141 - Atominstitut 
Publication Type: Thesis
Appears in Collections:Thesis

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