359 research outputs found
Minimal Models of Integrable Lattice Theory and Truncated Functional Equations
We consider the integrable XXZ model with the special open boundary
conditions. We perform Quantum Group reduction of this model in roots of unity
and use it for the definition Minimal Models of Interable lattice theory. It is
shown that after this Quantum Group reduction Sklyanin's transfer-matrices
satisfy the closed system of the truncated functional relations. We solve these
equations for the simplest case.Comment: 9 pages, LaTeX, corrected some typos, added some reference
Symplectic structures associated to Lie-Poisson groups
The Lie-Poisson analogues of the cotangent bundle and coadjoint orbits of a
Lie group are considered. For the natural Poisson brackets the symplectic
leaves in these manifolds are classified and the corresponding symplectic forms
are described. Thus the construction of the Kirillov symplectic form is
generalized for Lie-Poisson groups.Comment: 30 page
Functional Relations and Analytic Bethe Ansatz for Twisted Quantum Affine Algebras
Functional relations are proposed for transfer matrices of solvable vertex
models associated with the twisted quantum affine algebras
where
and . Their solutions are obtained for and conjectured
for in the dressed vacuum form in the analytic Bethe ansatz.Comment: 14 pages. Plain Te
Tensor operators and Wigner-Eckart theorem for the quantum superalgebra U_{q}[osp(1\mid 2)]
Tensor operators in graded representations of Z_{2}-graded Hopf algebras are
defined and their elementary properties are derived. Wigner-Eckart theorem for
irreducible tensor operators for U_{q}[osp(1\mid 2)] is proven. Examples of
tensor operators in the irreducible representation space of Hopf algebra
U_{q}[osp(1\mid 2)] are considered. The reduced matrix elements for the
irreducible tensor operators are calculated. A construction of some elements of
the center of U_{q}[osp(1\mid 2)] is given.Comment: 16 pages, Late
Symplectic structure of the moduli space of flat connections on a Riemann surface
We consider canonical symplectic structure on the moduli space of flat
{\g}-connections on a Riemann surface of genus with marked points.
For {\g} being a semisimple Lie algebra we obtain an explicit efficient
formula for this symplectic form and prove that it may be represented as a sum
of copies of Kirillov symplectic form on the orbit of dressing
transformations in the Poisson-Lie group and copies of the
symplectic structure on the Heisenberg double of the Poisson-Lie group (the
pair () corresponds to the Lie algebra {\g}).Comment: 20 page
On the Integrable Structure of the Ising Model
Starting from the lattice realization of the Ising model defined on a
strip with integrable boundary conditions, the exact spectrum (including
excited states) of all the local integrals of motion is derived in the
continuum limit by means of TBA techniques. It is also possible to follow the
massive flow of this spectrum between the UV conformal fixed point and
the massive IR theory. The UV expression of the eigenstates of such integrals
of motion in terms of Virasoro modes is found to have only rational
coefficients and their fermionic representation turns out to be simply related
to the quantum numbers describing the spectrum.Comment: 18 pages, no figure
Further solutions of critical ABF RSOS models
The restricted SOS model of Andrews, Baxter and Forrester has been studied.
The finite size corrections to the eigenvalue spectra of the transfer matrix of
the model with a more general crossing parameter have been calculated.
Therefore the conformal weights and the central charges of the non-unitary or
unitary minimal conformal field have been extracted from the finite size
corrections.Comment: Pages 11; revised versio
Bethe Equations "on the Wrong Side of Equator"
We analyse the famous Baxter's equations for () spin chain
and show that apart from its usual polynomial (trigonometric) solution, which
provides the solution of Bethe-Ansatz equations, there exists also the second
solution which should corresponds to Bethe-Ansatz beyond . This second
solution of Baxter's equation plays essential role and together with the first
one gives rise to all fusion relations.Comment: 13 pages, original paper was spoiled during transmissio
Kinematics of a relativistic particle with de Sitter momentum space
We discuss kinematical properties of a free relativistic particle with
deformed phase space in which momentum space is given by (a submanifold of) de
Sitter space. We provide a detailed derivation of the action, Hamiltonian
structure and equations of motion for such free particle. We study the action
of deformed relativistic symmetries on the phase space and derive explicit
formulas for the action of the deformed Poincare' group. Finally we provide a
discussion on parametrization of the particle worldlines stressing analogies
and differences with ordinary relativistic kinematics.Comment: RevTeX, 12 pages, no figure
Branching rules of semi-simple Lie algebras using affine extensions
We present a closed formula for the branching coefficients of an embedding p
in g of two finite-dimensional semi-simple Lie algebras. The formula is based
on the untwisted affine extension of p. It leads to an alternative proof of a
simple algorithm for the computation of branching rules which is an analog of
the Racah-Speiser algorithm for tensor products. We present some simple
applications and describe how integral representations for branching
coefficients can be obtained. In the last part we comment on the relation of
our approach to the theory of NIM-reps of the fusion rings of WZW models with
chiral algebra g_k. In fact, it turns out that for these models each embedding
p in g induces a NIM-rep at level k to infinity. In cases where these NIM-reps
can be be extended to finite level, we obtain a Verlinde-like formula for
branching coefficients.Comment: 11 pages, LaTeX, v2: one reference added, v3: Clarified proof of
Theorem 2, completely rewrote and extended Section 5 (relation to CFT), added
various references. Accepted for publication in J. Phys.
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