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Differential Geometrical Methods in Theoretical Physics (Hardcover, 1988 ed.)
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Differential Geometrical Methods in Theoretical Physics (Hardcover, 1988 ed.)
Series: NATO Science Series C, 250
Expected to ship within 10 - 15 working days
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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.
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