TY - THES
T1 - The Quark Sector of the QCD Ground State in Coulomb Gauge
A1 - Pak,Markus
Y1 - 2012/11/02
N2 - This thesis is divided into two parts concerning the two unresolved issues of QCD. In Part I we investigate chiral symmetry breaking. We concentrate on the fermionic content of the QCD Lagrangian, since chiral symmetry is a property of the quark sector. In Part II we turn to the issue of color confinement and compute the potential between a pair of infinitely heavy quarks from the so-called Wilson loop. Here we deal with pure gluodynamics, since color confinement is encoded in the gluon sector of QCD.
The first part of the thesis concerns the inclusion of dynamical quarks into the variational approach to QCD in Coulomb gauge. It has been known for thirty years that an ansatz for the quark vacuum wave functional mimicking BCS theory,
although successful on a qualitative level, is not sufficient to generate the right amount of dynamical chiral symmetry breaking to account for the dynamical nucleon mass - the value of the chiral condensate is by a factor of two too low.
We identify the missing piece as the coupling of the quarks to the transverse gluons. We generalize the BCS-ansatz and include the coupling of the quarks to the transverse gauge field into the quark vacuum wave functional. We find this coupling to increase the chiral condensate substantially and to bring the dynamical mass into the region of experiment.
In Part II we turn to a method to approach the Wilson loop in a continuum formulation which has been suggested years ago for supersymmetric theories and has recently been applied to QCD in Landau gauge. All planar ladder diagrams connecting the two temporal paths of the Wilson loop are summed to give a Dyson equation, which, at least in an approximate fashion, accounts for path ordering.
This Dyson equation is critically reviewed, its range of applicability in non-supersymmetric gauge theories discussed and applied to Coulomb gauge gluon propagators. We compute the Wilson loop for the temporal gluon propagator as well as the spatial gluon propagator. We find for the spatial Wilson loop results which are qualitatively, but not quantitatively, significant. We find a static quark potential which shows both a Coulombic as well as a confining region; however, the string tension extracted from the slope of the linear
potential is too large compared to the string tension obtained in lattice QCD.
KW - Coulomb-Eichung
KW - Quark
KW - Quarkconfinement
KW - Symmetriebrechung
KW - Quantenchromodynamik
CY - Tübingen
PB - Universitätsbibliothek Tübingen
AD - Wilhelmstr. 32, 72074 Tübingen
UR - http://tobias-lib.uni-tuebingen.de/volltexte/2012/6491
ER -