139 research outputs found
Local Operators in Massive Quantum Field Theories
Contribution to the proceedings of Schladming 1995. A review of the form
factor approach and its utilisation to determine the space of local operators
of integrable massive quantum theories is given. A few applications are
discussed.Comment: 6 pages, late
Asymptotic factorisation of form factors in two-dimensional quantum field theory
It is shown that the scaling operators in the conformal limit of a
two-dimensional field theory have massive form factors which obey a simple
factorisation property in rapidity space. This has been used to identify such
operators within the form factor bootstrap approach. A sum rule which yields
the scaling dimension of such operators is also derived.Comment: 11 pages, late
Correlation Functions in the Two-dimensional Ising Model in a Magnetic Field at
The one and two-particle form factors of the energy operator in the
two-dimensional Ising model in a magnetic field at are exactly computed
within the form factor bootstrap approach. Together with the matrix elements of
the magnetisation operator already computed in ref.\,\cite{immf}, they are used
to write down the large distance expansion for the correlators of the two
relevant fields of the model.Comment: 18 pages, latex, 7 table
Form Factors of the Elementary Field in the Bullough-Dodd Model
We derive the recursive equations for the form factors of the local hermitian
operators in the Bullough-Dodd model. At the self-dual point of the theory, the
form factors of the fundamental field of the Bullough-Dodd model are equal to
those of the fundamental field of the Sinh-Gordon model at a specific value of
the coupling constant.Comment: 14 pages, LATEX file, ISAS/EP/92/208;USP-IFQSC/TH/92-5
Non-integrable Quantum Field Theories as Perturbations of Certain Integrable Models
We approach the study of non--integrable models of two--dimensional quantum
field theory as perturbations of the integrable ones. By exploiting the
knowledge of the exact -matrix and Form Factors of the integrable field
theories we obtain the first order corrections to the mass ratios, the vacuum
energy density and the -matrix of the non-integrable theories. As
interesting applications of the formalism, we study the scaling region of the
Ising model in an external magnetic field at and the scaling
region around the minimal model . For these models, a remarkable
agreement is observed between the theoretical predictions and the data
extracted by a numerical diagonalization of their Hamiltonian.Comment: 60 pages, latex, 9 figure
On the third level descendent fields in the Bullough-Dodd model and its reductions
Exact vacuum expectation values of the third level descendent fields
in the Bullough-Dodd model
are proposed. By performing quantum group restrictions, we obtain in perturbed minimal conformal field theories.Comment: 7 pages, LaTeX file with amssymb; to appear in Phys. Lett.
Towards the Construction of Wightman Functions of Integrable Quantum Field Theories
The purpose of the ``bootstrap program'' for integrable quantum field
theories in 1+1 dimensions is to construct a model in terms of its Wightman
functions explicitly. In this article, this program is mainly illustrated in
terms of the sine-Gordon and the sinh-Gordon model and (as an exercise) the
scaling Ising model. We review some previous results on sine-Gordon breather
form factors and quantum operator equations. The problem to sum over
intermediate states is attacked in the short distance limit of the two point
Wightman function for the sinh-Gordon and the scaling Ising model.Comment: LATEX 18 pages, Talk presented at the '6th International Workshop on
Conformal Field Theories and Integrable Models', in Chernologka, September
200
Exact S-matrices for supersymmetric sigma models and the Potts model
We study the algebraic formulation of exact factorizable S-matrices for
integrable two-dimensional field theories. We show that different formulations
of the S-matrices for the Potts field theory are essentially equivalent, in the
sense that they can be expressed in the same way as elements of the
Temperley-Lieb algebra, in various representations. This enables us to
construct the S-matrices for certain nonlinear sigma models that are invariant
under the Lie ``supersymmetry'' algebras sl(m+n|n) (m=1,2; n>0), both for the
bulk and for the boundary, simply by using another representation of the same
algebra. These S-matrices represent the perturbation of the conformal theory at
theta=pi by a small change in the topological angle theta. The m=1, n=1 theory
has applications to the spin quantum Hall transition in disordered fermion
systems. We also find S-matrices describing the flow from weak to strong
coupling, both for theta=0 and theta=pi, in certain other supersymmetric sigma
models.Comment: 32 pages, 8 figure
Scattering Theory and Correlation Functions in Statistical Models with a Line of Defect
The scattering theory of the integrable statistical models can be generalized
to the case of systems with extended lines of defect. This is done by adding
the reflection and transmission amplitudes for the interactions with the line
of inhomegeneity to the scattering amplitudes in the bulk. The factorization
condition for the new amplitudes gives rise to a set of Reflection-Transmission
equations. The solutions of these equations in the case of diagonal -matrix
in the bulk are only those with . The choice corresponds to
the Ising model. We compute the exact expressions of the transmission and
reflection amplitudes relative to the interaction of the Majorana fermion of
the Ising model with the defect. These amplitudes present a weak-strong duality
in the coupling constant, the self-dual points being the special values where
the defect line acts as a reflecting surface. We also discuss the bosonic case
which presents instability properties and resonance states. Multi-defect
systems which may give rise to a band structure are also considered. The exact
expressions of correlation functions is obtained in terms of Form Factors of
the bulk theory and matrix elements of the defect operator.Comment: 50 pages, LATEX file, ISAS/EP/94-12
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