Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Physics and Astronomy

First Advisor

Richard W. Haymaker


The strong interactions between quarks are believed to be described by Quantum Chromodynamics (QCD), which is a non-abelian SU(3) gauge theory. It is known that QCD undergoes a deconfining phase transition at very high temperatures, that is, at low temperatures QCD is in a confined phase, at sufficient high temperatures it is in a unconfined phase. Also, quark confinement is believed to be due to the string formation. In this dissertation we studied SU(2) gauge theory using numerical methods of LGT, which will provide some insights about the properties of QCD because SU(2) is similar to SU(3). We measured the flux distributions of a q q pair at various temperatures in different volumes. We find that in the limit of infinite volumes the flux distribution is different in the two phases. In the confined phase strong evidence is found for the string formation, however, in the unconfined phase there is no string formation. On the other hand, in the limit of zero temperature and finite volumes we find clear signal for string formation in the large volume region, however, the string tension measured in intermediate volumes is due to finite volume effects, there is no intrinsic string formation. The color flux energies (action) of the q q pair are described by Michael sum rules. The original Michael sum rules deal with a static q q pair at zero temperature in infinite volumes. To check these sum rules with our flux data at finite temperatures, we present a complete derivation for the sum rules, then generalize them to account for finite temperature effects. We find that our flux data are consistent with the prediction of generalized sum rules. Our study elucidates the rich structures of QCD, and provides evidences for the quark confinement and string formation. This supports the belief that QCD is a correct theory for strong interactions, and quark confinement can be explained by QCD.