448 research outputs found
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 of the SU(N) Gross-Neveu model and 1/N expansion
The general SU(N) form factor formula is constructed. Exact form factors for
the field, the energy momentum and the current operators are derived and
compared with the 1/N-expansion of the chiral Gross-Neveu model and full
agreement is found. As an application of the form factor approach the equal
time commutation rules of arbitrary local fields are derived and in general
anyonic behavior is found.Comment: 35 pages Published version of the paper, which includes minor
corrections and improved acknowledgement
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
Quantum Group Invariant Integrable n-State Vertex Models with Periodic Boundary Conditions
An invariant transfer matrix with periodic boundary conditions
is analysed by means of the algebraic nested Bethe ansatz for the case of
being a root of unity. The transfer matrix corresponds to a 2-dimensional
vertex model on a torus with topological interaction w.r.t. the 3-dimensional
interior of the torus. By means of finite size analysis we find the central
charge of the corresponding Virasoro algebra as .Comment: 19 page
Two-point Correlation Function in Integrable QFT with Anti-Crossing Symmetry
The two-point correlation function of the stress-energy tensor for the
massive deformation of the non-unitary model is
computed. We compare the ultraviolet CFT perturbative expansion of this
correlation function with its spectral representation given by a summation over
matrix elements of the intermediate asymptotic massive particles. The fast rate
of convergence of both approaches provides an explicit example of an accurate
interpolation between the infrared and ultraviolet behaviours of a Quantum
Field Theory.Comment: 9 pages, LATEX file, ISAS/EP/93/167 (The paper contains two figures:
extract them separately with the name fig1.ps and fig2.ps and then LATEX
twice the paper
Completeness of ``Good'' Bethe Ansatz Solutions of a Quantum Group Invariant Heisenberg Model
The -quantum group invariant spin 1/2 XXZ-Heisenberg model with open
boundary conditions is investigated by means of the Bethe ansatz. As is well
known, quantum groups for equal to a root of unity possess a finite number
of ``good'' representations with non-zero q-dimension and ``bad'' ones with
vanishing q-dimension. Correspondingly, the state space of an invariant
Heisenberg chain decomposes into ``good'' and ``bad'' states. A ``good'' state
may be described by a path of only ``good'' representations. It is shown that
the ``good'' states are given by all ``good'' Bethe ansatz solutions with roots
restricted to the first periodicity strip, i.e. only positive parity strings
(in the language of Takahashi) are allowed. Applying Bethe's string counting
technique completeness of the ``good'' Bethe states is proven, i.e. the same
number of states is found as the number of all restricted path's on the
-Bratteli diagram. It is the first time that a ``completeness" proof
for an anisotropic quantum invariant reduced Heisenberg model is performed.Comment: LaTeX file with LaTeX figures, 24 pages, 1 PiCTeX figur
Exact form factors in integrable quantum field theories: the scaling Z(N)-Ising model
A general form factor formula for the scaling Z(N)-Ising model is
constructed. Exact expressions for matrix elements are obtained for several
local operators. In addition, the commutation rules for order, disorder
parameters and para-Fermi fields are derived. Because of the unusual statistics
of the fields, the quantum field theory seems to be not related to any
classical Lagrangian or field equation.Comment: 36 page
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