4 research outputs found
Constructing Infinite Particle Spectra
We propose a general construction principle which allows to include an
infinite number of resonance states into a scattering matrix of hyperbolic
type. As a concrete realization of this mechanism we provide new S-matrices
generalizing a class of hyperbolic ones, which are related to a pair of simple
Lie algebras, to the elliptic case. For specific choices of the algebras we
propose elliptic generalizations of affine Toda field theories and the
homogeneous sine-Gordon models. For the generalization of the sinh-Gordon model
we compute explicitly renormalization group scaling functions by means of the
c-theorem and the thermodynamic Bethe ansatz. In particular we identify the
Virasoro central charges of the corresponding ultraviolet conformal field
theories.Comment: 7 pages Latex, 7 figures (typo in figure 3 corrected
On the Construction of Quantum Field Theories with Factorizing S-Matrices
The subject of this thesis is a novel construction method for interacting
relativistic quantum field theories on two-dimensional Minkowski space. The
input in this construction is not a classical Lagrangian, but rather a
prescribed factorizing S-matrix, i.e. the inverse scattering problem for such
quantum field theories is studied.
For a large class of factorizing S-matrices, certain associated quantum
fields, which are localized in wedge-shaped regions of Minkowski space, are
constructed explicitely. With the help of these fields, the local observable
content of the corresponding model is defined and analyzed by employing methods
from the algebraic framework of quantum field theory.
The abstract problem in this analysis amounts to the question under which
conditions an algebra of wedge-localized observables can be used to generate a
net of local observable algebras with the right physical properties. The answer
given here uses the so-called modular nuclearity condition, which is shown to
imply the existence of local observables and the Reeh-Schlieder property.
In the analysis of the concrete models, this condition is proven for a large
family of S-matrices, including the scattering operators of the Sinh-Gordon
model and the scaling Ising model as special examples. The so constructed
models are then investigated with respect to their scattering properties. They
are shown to solve the inverse scattering problem for the considered
S-matrices, and a proof of asymptotic completeness is given.Comment: PhD thesis, Goettingen university, 2006 (advisor: D. Buchholz) 153
pages, 10 figure