Uses of the vacuum

Three problems in quantum field theory are analyzed. Each presents the vacuum in a different role. The connections among these significant roles are discussed in Chapter I. Chapter II contains a calculation of the zero-point energy in the Kaluza-Klein model. The zero-point fluctuations induce a potential which makes the compact dimensional contract. The effective potential is seen to be the four-dimensional version of the Casimir effect. Chapter III contains a Monte Carlo study of asymptotic freedom scales in lattice QCD. Two versions of SU(2) gauge theory, having different representations of the gauge group, are compared. A new method is used to calculate the ratio of scale parameters of the two theories. The method directly uses the weak-coupling behavior of the theories. The Monte-Carlo results are compared with perturbative calculations on the lattice, one of which is presented. They are in good agreement. Chapter IV applies the hypothesis of dimensional reduction to five-dimensional SU(2) and four-dimensional SO(3) lattice gauge theories. New analytic results for the strong- and weak-coupling limits are derived. Monte Carlo calculations show dimensional reduction in the strong coupling phases of both theories. At the phase transition, the two theories show a similar loss of dimensional reduction. An external source of random flux does not induce dimensional reduction where it is not already present