Monte Carlo Methods in Quantum Field Theory

Several topics in Monte Carlo analysis are investigated, with the intent to improve some present methods as well as to find new applications. Chapter I provides a short introduction to Monte Carlo methods. In Chapter II, the problem of estimating the errors on Monte Carlo measurements is discussed. An accurate algorithm for estimating the errors is derived. Chapter III studies a generalization of the Heat Bath algorithm for quadratic and multi-quadratic actions which allows the system to over-relax. It is found that over-relaxation can accelerate the convergence of certain measurements. Chapter IV discusses the problem of Monte Carlo measurement of Effective Potentials. Chapter V presents a real Monte Carlo application, in which an upper bound is calculated for the mass of the Higgs particle in the Weinberg-Salam model of the weak and electromagnetic interactions. Treating the Weinberg-Salam model as an effective theory and simulating the Higgs sector via Monte Carlo leads to the conclusion that the mass of the Higgs particle must be less than 790 GeV.