Topological Quantum Field Theory and Pure Yang-Mills Dynamics

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. To appear in the Proceedings of the Third International Workshop on Contemporary Problems in Mathematical Physics (COPROMAPH3), 1st-7th November 2003, Cotonou (Republic of Benin), 21 pages