| This dissertation discusses two problems in non-perturbative methods in elementary particle physics. It consists of two parts.; The first part is a research on the problem of Critical Slowing Down of Numerical Monte-Carlo simulations in lattice field theory. The problem is viewed as a consequence of the locality of the algorithms that are implemented. It is shown that a certain class of generalizations of over-relaxation algorithms is incapable to further reduce the dynamical exponent z below its standard over-relaxed value of {dollar}zapprox1.{dollar} The generalizations are obtained by viewing over-relaxation as a slightly deformed deterministic algorithm and should, therefore, hold for Hybrid Monte Carlo as well.; The second part is a study of non-perturbative effects in chiral Yukawa models. We consider the most general renormalizable chiral Yukawa model with {dollar}SU(3)sb{lcub}rm color{rcub}{dollar} replaced by {dollar}SU(Nsb{lcub}c{rcub}), SU(2)sb{lcub}rm L{rcub}{dollar} replaced by {dollar}SU(Nsb{lcub}w{rcub}){dollar} and {dollar}U(1)sb{lcub}Y{rcub}{dollar} replaced by {dollar}U(1)sp{lcub}Nsb{lcub}w{rcub}-1{rcub}{dollar} in the limit {dollar}Nsb{lcub}c{rcub}toinfty, Nsb{lcub}w{rcub}toinfty{dollar} with the ratio {dollar}{dollar}rho = sqrt{lcub}{lcub}Nsb{lcub}w{rcub}over Nsb{lcub}c{rcub}{rcub}{rcub}ne0, infty rm held fixed.{dollar}{dollar}Since for {dollar}Nsb{lcub}w{rcub}ge3{dollar} only one renormalizable Yukawa coupling per family exists and there is no mixing between families the limit is appropriate for the description of the effects of a heavy top quark when all the other fermions are taken to be massless. The large {dollar}N = sqrt{lcub}Nsb{lcub}c{rcub}Nsb{lcub}w{rcub}{rcub}{dollar} expansion is expected to be no worse quantitatively in this model that in the purely scalar case and the {dollar}N = infty{dollar} limit is soluble even when the model is regularized non-perturbatively. A rough estimate of the triviality bound on the Yukawa coupling is equivalent to {dollar}msb{lcub}t{rcub}le1 TeV.{dollar}... |
