Topological solitons - are of broad interest in physics. They are objects with
localised energy and stability ensured by their topological properties. It is
possible to create them during phase transitions which break some sym-
metry in a frustrated system. They are ubiquitous in condensed matter,
ranging from monopole excitations in spin ices to vortices in superconduc-
tors. In such situations, their behaviour has been extensively studied.
Less well understood and yet equally interesting are the symmetry-breaking
phase transitions that could produce topological defects is the early universe.
Grand unified theories generically admit the creation of cosmic strings and
monopoles, amongst other objects.
There is no reason to expect that the behaviour of such objects should be
classical or, indeed, supersymmetric, so to fully understand the behaviour
of these theories it is necessary to study the quantum properties of the
associated topological defects. Unfortunately, the standard analytical tools
for studying quantum field theory - including perturbation theory - do not
work so well when applied to topological defects.
Motivated by this realisation, this thesis presents numerical techniques for
the study of topological solitons in quantum field theory. Calculations are
carried out nonperturbatively within the framework of lattice Monte Carlo
simulations. Methods are demonstrated which use correlation functions to
study the mass, interaction form factors, dispersion relations and excitations
of quantum topological solitons. Results are compared to exact expressions
obtained from integrability, and to previous work using less sophisticated
numerical techniques.
The techniques developed are applied to the prototypical kink soliton and
to the 't Hooft-Polyakov monopole.