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Stephenson, David Brian

English

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

Non-perturbative field theories

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