Monopoles and U(1) lattice gauge theory

In this thesis, I describe calculations done in $U(1)$ lattice gauge theory. After reviewing general concepts for doing calculations using quantum field theory on a space-time lattice, I discuss the presence of topological objects, which correspond to local minima of the action. These topological objects are identified as magnetic monopoles. Using configurations of monopoles identified in gauge field simulations in four dimensions, I study the behavior of the monopoles near the confinement-deconfinement transition.In order to understand how quantitative calculations may be performed using the monopoles, I have performed numerical simulations of the gauge fields in three dimensions and extracted monopole configurations. Using a calculational scheme developed in this thesis, these monopole configurations are used to calculate the static potential between two quarks. The results are compared with answers obtained using semi-classical methods.U of I OnlyETDs are only available to UIUC Users without author permissio