After almost half a century of existence the main question about quantum
field theory seems still to be: what does it really describe? and not
yet: does it provide a good description of nature? J. A. Swieca Ever
since quantum field theory has been applied to strong int- actions,
physicists have tried to obtain a nonperturbative und- standing.
Dispersion theoretic sum rules, the S-matrix bootstrap, the dual models
(and their reformulation in string language) and s the conformal
bootstrap of the 70 are prominent cornerstones on this thorny path.
Furthermore instantons and topological solitons have shed some light on
the nonperturbati ve vacuum structure respectively on the existence of
nonperturbative "charge" s- tors. To these attempts an additional one
was recently added', which is yet not easily describable in terms of one
"catch phrase". Dif- rent from previous attempts, it is almost entirely
based on new noncommutative algebraic structures: "exchange algebras"
whose "structure constants" are braid matrices which generate a ho-
morphism of the infini te (inducti ve limi t) Artin braid group Boo into
a von Neumann algebra. Mathematically there is a close 2 relation to
recent work of Jones - Its physical origin is the resul t of a subtle
analysis of Ei nstein causality expressed in terms of local commutati vi
ty of space-li ke separated fields. It is most clearly recognizable in
conformal invariant quantum field theories.