219 research outputs found
The Gervais-Neveu-Felder equation and the quantum Calogero-Moser systems
We quantize the spin Calogero-Moser model in the -matrix formalism. The
quantum -matrix of the model is dynamical. This -matrix has already
appeared in Gervais-Neveu's quantization of Toda field theory and in Felder's
quantization of the Knizhnik-Zamolodchikov-Bernard equation.Comment: Comments and References adde
On the Space of KdV Fields
The space of functions A over the phase space of KdV-hierarchy is studied as
a module over the ring D generated by commuting derivations. A D-free
resolution of A is constructed by Babelon, Bernard and Smirnov by taking the
classical limit of the construction in quantum integrable models assuming a
certain conjecture. We propose another D-free resolution of A by extending the
construction in the classical finite dimensional integrable system associated
with a certain family of hyperelliptic curves to infinite dimension assuming a
similar conjecture. The relation of two constructions is given.Comment: 13 page
Integrability and Conformal Symmetry in Higher Dimensions: A Model with Exact Hopfion Solutions
We use ideas on integrability in higher dimensions to define Lorentz
invariant field theories with an infinite number of local conserved currents.
The models considered have a two dimensional target space. Requiring the
existence of Lagrangean and the stability of static solutions singles out a
class of models which have an additional conformal symmetry. That is used to
explain the existence of an ansatz leading to solutions with non trivial Hopf
charges.Comment: 30 pages, plain late
Form factors of the XXZ model and the affine quantum group symmetry
We present new expressions of form factors of the XXZ model which satisfy
Smirnov's three axioms. These new form factors are obtained by acting the
affine quantum group to the known ones obtained
in our previous works. We also find the relations among all the new and known
form factors, i.e., all other form factors can be expressed as kind of
descendents of a special one.Comment: 11 pages, latex; Some explanation is adde
Null-vectors in Integrable Field Theory
The form factor bootstrap approach allows to construct the space of local
fields in the massive restricted sine-Gordon model. This space has to be
isomorphic to that of the corresponding minimal model of conformal field
theory. We describe the subspaces which correspond to the Verma modules of
primary fields in terms of the commutative algebra of local integrals of motion
and of a fermion (Neveu-Schwarz or Ramond depending on the particular primary
field). The description of null-vectors relies on the relation between form
factors and deformed hyper-elliptic integrals. The null-vectors correspond to
the deformed exact forms and to the deformed Riemann bilinear identity. In the
operator language, the null-vectors are created by the action of two operators
\CQ (linear in the fermion) and \CC (quadratic in the fermion). We show
that by factorizing out the null-vectors one gets the space of operators with
the correct character. In the classical limit, using the operators \CQ and
\CC we obtain a new, very compact, description of the KdV hierarchy. We also
discuss a beautiful relation with the method of Whitham.Comment: 36 pages, Late
On the Quantum Inverse Problem for the Closed Toda Chain
We reconstruct the canonical operators of the quantum closed Toda
chain in terms of Sklyanin's separated variables.Comment: 16 page
Quantization of Solitons and the Restricted Sine-Gordon Model
We show how to compute form factors, matrix elements of local fields, in the
restricted sine-Gordon model, at the reflectionless points, by quantizing
solitons. We introduce (quantum) separated variables in which the Hamiltonians
are expressed in terms of (quantum) tau-functions. We explicitly describe the
soliton wave functions, and we explain how the restriction is related to an
unusual hermitian structure. We also present a semi-classical analysis which
enlightens the fact that the restricted sine-Gordon model corresponds to an
analytical continuation of the sine-Gordon model, intermediate between
sine-Gordon and KdV.Comment: 29 pages, Latex, minor updatin
Ring-shaped exact Hopf solitons
The existence of ring-like structures in exact hopfion solutions is shown.Comment: version accepted for publication in JMP, includes symmetry
transformation for finite paramete
Toroidal Soliton Solutions in O(3)^N Nonlinear Sigma Model
A set of N three component unit scalar fields in (3+1) Minkowski space-time
is investigated. The highly nonlinear coupling between them is chosen to omit
the scaling instabilities. The multi-soliton static configurations with
arbitrary Hopf numbers are found. Moreover, the generalized version of the
Vakulenko-Kapitansky inequality is obtained. The possibility of attractive,
repulsing and noninteracting channels is discussed.Comment: to be published in Mod. Phys. Lett.
Integrable subsystem of Yang--Mills dilaton theory
With the help of the Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2)
Yang-Mills field, we find an integrable subsystem of SU(2) Yang-Mills theory
coupled to the dilaton. Here integrability means the existence of infinitely
many symmetries and infinitely many conserved currents. Further, we construct
infinitely many static solutions of this integrable subsystem. These solutions
can be identified with certain limiting solutions of the full system, which
have been found previously in the context of numerical investigations of the
Yang-Mills dilaton theory. In addition, we derive a Bogomolny bound for the
integrable subsystem and show that our static solutions are, in fact, Bogomolny
solutions. This explains the linear growth of their energies with the
topological charge, which has been observed previously. Finally, we discuss
some generalisations.Comment: 25 pages, LaTex. Version 3: appendix added where the equivalence of
the field equations for the full model and the submodel is demonstrated;
references and some comments adde
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