Algebraic Quantum Field Theory: A Status Report
Buchholz, Detlev
Algebraic quantum field theory is an approach to relativistic
quantum physics, notably the theory of elementary particles,
which complements other modern developments in this field.
It is particularly powerful for structural analysis but has also
proven to be useful in the rigorous treatment of models.
In this contribution a non-technical survey is given
with emphasis on interesting recent developments and future
perspectives. Topics covered are the relation between the
algebraic approach and conventional quantum field theory,
its significance for the resolution of conceptual problems
(such as the revision of the particle concept)
and its role in the characterization and possibly also
construction of quantum field theories with the help of
modular theory. The algebraic approach has also shed
new light on the treatment of quantum field theories on curved
spacetime and made contact with recent developments in
string theory (algebraic holography).
Reference: Plenary talk given at 13th International Congress in Mathematical
Physics (ICMP 2000), London, July 2000.
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Last modified: Don Feb 6 17:02:28 CET 2003