| Speaker: | Stepehen J. Summers |
| Title: | Modular Structure and the Construction of Quantum Field Models |
| Abstract: | Algebraic quantum field theory has begun to contribute ideas
to one of the most difficult and important problems in
mathematical quantum field theory --- the construction of
models. I shall report on some of these ideas. One approach
makes an intriguing use of an intrinsic modular localization
to construct nets of observable algebras from the initial
data of a positive energy representation of the Poincare
group without direct appeal to quantum fields. Another
development has been motivated by integrable quantum field
models with factorizable scattering matrix in two space-time
dimensions. In this approach, relatively easily
constructible models of nonlocal quantum fields are used to
obtain local observable algebras by purely algebraic means,
avoiding the necessity of directly constructing the local
quantum fields, which are significantly more complicated
objects than the initial nonlocal fields. In all these
approaches Tomita-Takesaki modular theory is essential.
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