Rigorous quantum field theory models

Quantum Solution to Scalar Field Theory Models

Amplitudes A n in d-dimensional scalar field theory are generated, to all orders in the coupling constant and at n-point. The amplitudes are expressed as a series in the mass m and coupling λ. The inputs are the classical scattering, and these generate, after the integrals are performed, the series expansion in the couplings λ i. The group theory of the scalar field theory leads to an additiona...

Network models of quantum percolation and their field-theory representations.

We obtain the field-theory representations of several network models that are relevant to 2D transport in high magnetic fields. Among them, the simplest one, which is relevant to the plateau transition in the quantum Hall effect, is equivalent to a particular representation of an antiferromagnetic SU(2N) (N → 0) spin chain. Since the later can be mapped onto a θ 6= 0, U(2N)/U(N)×U(N) sigma mode...

Lattice Versions of Quantum Field Theory Models in Two Dimensions

Correlators in integrable quantum field theory . The scaling RSOS models

The study of the scaling limit of two-dimensional models of statistical mechanics within the framework of integrable field theory is illustrated through the example of the RSOS models. Starting from the exact description of regime III in terms of colliding particles, we compute the correlation functions of the thermal, ϕ 1,2 and (for some cases) spin operators in the two-particle approximation....

Algebraic constructive quantum field theory: Integrable models and deformation techniques

Several related operator-algebraic constructions for quantum field theory models on Minkowski spacetime are reviewed. The common theme of these constructions is that of a Borchers triple, capturing the structure of observables localized in a Rindler wedge. After reviewing the abstract setting, we discuss in this framework i) the construction of free field theories from standard pairs, ii) the i...