185 research outputs found
The "Bootstrap Program" for Integrable Quantum Field Theories in 1+1 Dim
The purpose of the "bootstrap program" is to construct integrable quantum
field theories in 1+1 dimensions in terms of their Wightman functions
explicitly. As an input the integrability and general assumptions of local
quantum field theories are used. The object is to be achieved in tree steps: 1)
The S-matrix is obtained using a qualitative knowledge of the particle spectrum
and the Yang-Baxter equations. 2) Matrix elements of local operators are
calculated by means of the "form factor program" using the S-matrix as an
input. 3) The Wightman functions are calculated by taking sums over
intermediate states. The first step has been performed for a large number of
models and also the second one for several models. The third step is unsolved
up to now. Here the program is illustrated in terms of the sine-Gordon model
alias the massive Thirring model. Exploiting the "off-shell" Bethe Ansatz we
propose general formulae for form factors. For example the n-particle matrix
element for all higher currents are given and in particular all eigenvalues of
the higher conserved charges are calculated. Furthermore quantum operator
equations are obtained in terms of their matrix elements, in particular the
quantum sine-Gordon field equation. Exact expressions for the finite wave
function and mass renormalization constants are calculated.Comment: Latex, 23 page
The nested SU(N) off-shell Bethe ansatz and exact form factors
The form factor equations are solved for an SU(N) invariant S-matrix under
the assumption that the anti-particle is identified with the bound state of N-1
particles. The solution is obtained explicitly in terms of the nested off-shell
Bethe ansatz where the contribution from each level is written in terms of
multiple contour integrals.Comment: This work is dedicated to the 75th anniversary of H. Bethe's
foundational work on the Heisenberg chai
SU(N) Matrix Difference Equations and a Nested Bethe Ansatz
A system of SU(N)-matrix difference equations is solved by means of a nested
version of a generalized Bethe Ansatz, also called "off shell" Bethe Ansatz.
The highest weight property of the solutions is proved. (Part I of a series of
articles on the generalized nested Bethe Ansatz and difference equations.)Comment: 18 pages, LaTe
Exact form factors in integrable quantum field theories: the sine-Gordon model (II)
A general model independent approach using the `off-shell Bethe Ansatz' is
presented to obtain an integral representation of generalized form factors. The
general techniques are applied to the quantum sine-Gordon model alias the
massive Thirring model. Exact expressions of all matrix elements are obtained
for several local operators. In particular soliton form factors of charge-less
operators as for example all higher currents are investigated. It turns out
that the various local operators correspond to specific scalar functions called
p-functions. The identification of the local operators is performed. In
particular the exact results are checked with Feynman graph expansion and full
agreement is found. Furthermore all eigenvalues of the infinitely many
conserved charges are calculated and the results agree with what is expected
from the classical case. Within the frame work of integrable quantum field
theories a general model independent `crossing' formula is derived. Furthermore
the `bound state intertwiners' are introduced and the bound state form factors
are investigated. The general results are again applied to the sine-Gordon
model. The integrations are performed and in particular for the lowest
breathers a simple formula for generalized form factors is obtained.Comment: LaTeX, 53 pages, Corrected typo
Exact form factors for the scaling Z{N}-Ising and the affine A{N-1}-Toda quantum field theories
Previous results on form factors for the scaling Ising and the sinh-Gordon
models are extended to general -Ising and affine -Toda quantum
field theories. In particular result for order, disorder parameters and
para-fermi fields and are
presented for the -model. For the -Toda model all form factors
for exponentials of the Toda fields are proposed. The quantum field equation of
motion is proved and the mass and wave function renormalization are calculated
exactly.Comment: Latex, 11 page
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
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