Algebraic Structures in local QFT

Motivations and Physical Aims of Algebraic QFT

We present illustrations which show the usefulness of algebraic QFT. In particular in low-dimensional QFT, when Lagrangian quantization is not available or is useless (e.g. in chiral conformal theories), the algebraic method is beginning to reveal its strength. This work is dedicated to the memory of Claude Itzykson

Local Fields in Boundary Conformal QFT

Conformal field theory on the half-space x > 0 of Minkowski spacetime (“boundary CFT”) is analyzed from an algebraic point of view, clarifying in particular the algebraic structure of local algebras and the bi-localized charge structure of local fields. The field content and the admissible boundary conditions are characterized in terms of a non-local chiral field algebra.

Regularized Algebraic Nets for General Covariant QFT on Differentiable Manifolds

Quantum general relativity may be considered as generally covariant QFT on differentiable manifolds, without any a priori metric structure. The kinematically covariance group acts by general diffeomorphisms on the manifold and by automorphisms on the isotonic net of ∗-algebras encoding the QFT, while the algebra of observables is covariant under the dynamical subgroup of the general diffeomorph...

Coincidences between M(atrix) Theory and Algebraic Qft ?

This is a preliminary account of coincidences between algebraic QFT and some recent observations on \light cone quantization" and applications to \M" theory. The most surprising correspondence is that between the existence of wedge aaliated semiglobal eld coordinates without vacuum polarization and those light cone elds (on which \Matrix" theory is based) with analogous properties. There is als...

Algebraic Structures