Lattice gauge theory in curved spacetime - Villegas, Kristian Hauser A. (Institute of Physics, College of Science, University of the Philippines Diliman, 2015)
This thesis lays down the theoretical foundation for lattice gauge theory in curved spacetime. After reviewing gauge theory,lattice gauge theory, and quantum field theory in curved spacetime, the lattice gauge theory for curved spacetime is formulated. This is done by generalizing the Wilson link, line,and loop variables to hold in a discretized curve spacetime background.The discretized Wilson action for both gluon and quark fields are the derived. For quark fields, this is done by including the vierbeins and the spin connection in the discretization process. It is shown that this action reduces correctly to the generally covariant form in the continuum limit. Using the Wilson action, it is further shown analytically that for a general curved spacetime background, two non-abelian point charges are always color-confined. A sample Monte Carlo simulation is also provided The fermion-doubling problem is discussed in the specific case of Friedman-Robertson-Walker metric which models an expanding universe. For concreteness, a specific example of discretization of a spacetime region with Schwarzschild metric far from the horizon is given.