Scale Parameters for Finite Temperature Actions of Lattice Gauge Theories Coupled to Fermions

Lattice gauge theories have become a powerful and popular way of approximating continuum theories in particle physics. In particular, many researchers are now investigating non-perturbative aspects of continuum theories, such as confinement in quantum chromodynamics (QCD), by performing Monte Carlo simulations of lattice theories. Although most of the simulations to date have not been concerned with finite temperature, the possibility of a deconfining phase transition in QCD has prompted the need for a formulation of finite temperature lattice gauge theory which maintains as much of the symmetry of the continuum theory as possible. Furthermore, the effects of fermions must be more extensively studied in Monte Carlo simulations of QCD than has been done thus far. This thesis contains results which will aid researchers in these goals. Two different lattice finite-temperature actions are discussed which maintain Euclidean invariance to the one-loop level. Certain special cases have been mentioned elsewhere in the literature, but this thesis provides the first comprehensive discussion of both of these actions extended to include couplings to Susskind and Wilson lattice fermions at finite temperature. Furthermore, since dimensional quantities obtained in a Monte Carlo simulation are expressed in terms of the lattice scale parameter, (LAMDA)(,L), the relationship between this scale parameter and the corresponding parameter of the continuum theory is needed to interpret the results of such a simulation, and, accordingly, is presented here. The elegant lattice background field method is used to perform the calculation to the one-loop level. Analytical results are presented for both lattice actions with provisions for SU(N) gauge theories of arbitrary N coupled to an arbitrary number of Wilson or Susskind fermion flavors at arbitrary temperature. In addition, through numerical integration, the results have also been presented in tabular and graphical form for many special cases of interest. The most striking result is the large difference in both the magnitude and functional dependence on lattice asymmetry of the scale parameters for the two lattice actions. Implications for Monte Carlo simulations and some merits and drawbacks of each action are discussed.