Topics in the Standard Model of Elementary Particles

This work is made up of two parts. In the first part we study some field theory models with cutoff at a finite temperature. We expect the theory with a cutoff to reveal some new features. We study effective potential at one loop level (and also phase transitions) and find out critical temperature T_{rm c} as a function of cutoff wedge. One interesting finding is that with a sharp cutoff, T_{rm c} oscillates as a function of wedge, but varies smoothly (without oscillations) in the case of a smooth cutoff. This shows that a smooth cutoff (and not a sharp cutoff) is physically acceptable. We discuss four field theory models: phi^4, NJL, dual QCD and Gross-Neveu model. We determine the phase transition temperature and find out that it is below the cutoff wedge (at one loop level). This is physically satisfactory. In case of the NJL model, we also study the connection of pion decay constant f_pi and pion condensate <|{9}9 > with wedge and the coupling constant {cal G}. In the second part we discuss decay and production of a top quark. We investigate the effect of having a nonperturbative coupling between a top quark and a Higgs particle which may be different from the coupling given by the standard model for a sufficiently heavy top. For this purpose we study the amplitude of the Feynman diagram with a Higgs internal line with its one end connected to a top line.