Non-perturbative field theories

Abstract

Some non-perturbative aspects of field theories are studied by applying lattice gauge theory techniques.

The low-lying hadronic mass spectrum is calculated numerically using quenched lattice quantum chromodynaniics. The results of large numerical simulations performed on a distributed array processor are presented and analysed. Particular emphasis is stressed upon the understanding of systematic and statistical errors in the calculation. In addition, the pion decay constant and the chiral condensate are evaluated. An attempt is made to relate the numerical findings to the experimentally measured quantities. A pioneering attempt to understand Yukawa couplings is discussed. A toy Fermion-Higgs system is studied numerically on a transputer array.

Dynamical fermions are included in the investigation of the behaviour of the system over a wide range of Yukawa couplings. A phase diagram is found for the model which shows evidence of spontaneous chiral symmetry breaking transitions. Extensions of the model are discussed together with some speculations concerning the behaviour of Yukawa couplings in general.

The possibility of using the lattice as a model for space-time is investigated by studying the propagation of particles on a fractal lattice. In addition, the use of truncated fractals as novel regulators is studied numerically in the hope that the problem of fermion doubling will be alleviated.