\chapter*{Conclusions}

This thesis has studied the renormalisation of various quantities in
lattice QCD.  Renormalisation constants were computed non-perturbatively
for the current renormalisation constants $Z_A$ and $Z_V$, for the
Sheikholeslami--Wohlert action.  There is evidence that this would bring
previous estimates for pseudoscalar and vector meson decay constants
closer to their experimental values than the estimates obtained using
the perturbative values, but there is still considerable discrepancy ---
at least for the UKQCD collaboration's results.  Since this work was
done over 2 years ago, more recent results have since appeared using
more refined techniques and improved actions, for which the
corresponding renormalisation constants to a large extent have yet to be
computed. 


A study was also conducted of the mass dependence of $Z_V$, using
tadpole improved and non-improved actions, and different prescriptions
for the $\Op(a)$ improvement of the operators.  This was little more
than a study of the feasibility of the `new' action and prescription,
which had a positive outcome insofar as they are now both being used by
the UKQCD collaboration.

In chapter \ref{chap4}, a method is presented for studying the quark--gluon
vertex non-perturbatively and using it to extract a renormalised QCD
coupling.  The initial results of this are encouraging, although the
perturbative matching to $\bar{MS}$ and other renormalisation schemes
still has to be done in order to obtain physical predictions.  The
results are still hefted with large errors, especially $\Op(a)$ errors
from the quark field renormalisation constant, and this has to be
brought under control before more reliable estimates of the running
coupling $\alpha_s$ and the scale parameter $\Lambda_{QCD}$ can be
obtained. 
