Untersuchung der Struktur des QCD-Vakuums mit Hilfe von Overlap-Fermionen
2008230 pages
Supervisors:
Thesis: PhD - ,
- Freie U., Berlin
- Published: 2008
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Abstract: (Freie U., Berlin)
In this thesis we explore the structure of the QCD vacuum and the nature of
the chiral phase transition with the aid of overlap fermions. Since overlap
fermions implement exact chiral symmetry and the Atiyah-Singer index theorem
on the lattice, they are particularly well suited for investigations of the
chiral and topological aspects of the QCD vacuum. A variable cut-off with
respect to the eigenmodes of the overlap Dirac operator allows a separation of
the infrared nonperturbative degrees of freedom on the scale of the Lambda
parameter of QCD from ultraviolet fluctuations observable on the scale of the
lattice-cutoff. The primary goal of the thesis is to perform an investigation
of the infrared, long ranged aspects of the vacuum which are exposed by the
low-lying modes of the overlap Dirac operator. We have developed various tools
which allow us to characterise the structure and dimension of any density
embedded in the 4-dimensional space-time. By applying these tools both at low
temperature (T=0) to quenched QCD and in the vicinity of the high temperature
phase transition of full QCD, we are able to describe the structure of the
modes and of the topological charge density and to analyse the local
selfduality of the underlying gauge fields. The main numerical effort of the
thesis is the computation of the full topological charge density and of the
lowest O(100) eigenmodes of the overlap operator, which are used to extract
various topological observables.- quantum chromodynamics
- lattice gauge theory
- vacuum structure
- topological charge density
- finite-temperature QCD
- overlap fermions
- chiral phase transition
- chiral symmetry
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