  By considering specific limits in the gauge coupling constant of pure
Yang--Mills dynamics, it is shown how there exist topological quantum field
theory sectors in such systems defining nonperturbative topological
configurations of the gauge fields which could well play a vital role in the
confinement and chiral symmetry breaking phenomena of phenomenologically
realistic theories such as quantum chromodynamics, the theory for the strong
interactions of quarks and gluons. A general research programme along such
lines is outlined. A series of other topics of possible relevance, ranging from
particle phenomenology to the quest for the ultimate unification of all
interactions and matter including quantum gravity, are raised in passing. The
general discussion is illustrated through some simple examples in 0+1 and 1+1
dimensions, clearly showing the importance of properly accounting for quantum
topological properties of the physical and configuration spaces in gauge
theories based on compact gauge groups.
