# Algebraic Quantum Field Theory: A Status Report

November 27, 2000

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).

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