Topological Yang-Mills theory with the Belavin-Polyakov-Schwarz-Tyupkin
SU(2) instanton is solved completely, revealing an underlying multi-link
intersection theory. Link invariants are also shown to survive the coupling to
a certain kind of matter (hyperinstantons). The physical relevance of
topological field theory and its invariants is discovered. By embedding
topological Yang-Mills theory into pure Yang-Mills theory, it is shown that the
topological version TQFT of a quantum field theory QFT allows us to formulate
consistently the perturbative expansion of QFT in the topologically nontrivial
sectors. In particular, TQFT classifies the set of good measures over the
instanton moduli space and solves the inconsistency problems of the previous
approaches. The qualitatively new physical implications are pointed out. Link
numbers in QCD are related to a non abelian analogoue of the Aharonov-Bohm
effect.Comment: 23 pages, 1 figure. Revision: additional explanation