1,549 research outputs found
Gauge Conditions for the Constrained-WZNW--Toda Reductions
There is a constrained-WZNW--Toda theory for any simple Lie algebra equipped
with an integral gradation. It is explained how the different approaches to
these dynamical systems are related by gauge transformations. Combining Gauss
decompositions in relevent gauges, we unify formulae already derived, and
explictly determine the holomorphic expansion of the conformally reduced WZNW
solutions - whose restriction gives the solutions of the Toda equations. The
same takes place also for semi-integral gradations. Most of our conclusions are
also applicable to the affine Toda theories.Comment: 12 pages, no figure
Higher Grading Generalisations of the Toda Systems
In the present paper we obtain some integrable generalisations of the Toda
system generated by flat connection forms taking values in higher --grading subspaces of a simple Lie algebra, and construct their general
solutions. One may think of our systems as describing some new fields of the
matter type coupled to the standard Toda systems. This is of special interest
in nonabelian Toda theories where the latter involve black hole target space
metrics. We also give a derivation of our conformal system on the base of the
Hamiltonian reduction of the WZNW model; and discuss a relation between abelian
and nonabelian systems generated by a gauge transformation that maps the first
grading description to the second. The latter involves grades larger than one.Comment: 24 pages, latex, no figures; Expanded version accepted for
publication in Nuclear Physics
Quantum sl_n Toda field theories
We quantize Toda field theories in a periodic lattice. We find the
quantum exchange algebra in the diagonal monodromy (Bloch wave) basis in the
case of the defining representation. In the case we extend the analysis
also to the second fundamental representation. We clarify, in particular, the
relation of Jimbo and Rosso's quantum matrix with the quantum matrix in
the Bloch wave basis.Comment: 19 pages, SISSA-ISAS 110/92/E
Reactor power systems for manned earth orbital applications
Design requirements for reactor power system of manned earth orbital space statio
The Quantum Group Structure of 2D Gravity and Minimal Models II: The Genus-Zero Chiral Bootstrap
The F and B matrices associated with Virasoro null vectors are derived in
closed form by making use of the operator-approach suggested by the Liouville
theory, where the quantum-group symmetry is explicit. It is found that the
entries of the fusing and braiding matrices are not simply equal to
quantum-group symbols, but involve additional coupling constants whose
derivation is one aim of the present work. Our explicit formulae are new, to
our knowledge, in spite of the numerous studies of this problem. The
relationship between the quantum-group-invariant (of IRF type) and
quantum-group-covariant (of vertex type) chiral operator-algebras is fully
clarified, and connected with the transition to the shadow world for
quantum-group symbols. The corresponding 3-j-symbol dressing is shown to reduce
to the simpler transformation of Babelon and one of the author (J.-L. G.) in a
suitable infinite limit defined by analytic continuation. The above two types
of operators are found to coincide when applied to states with Liouville
momenta going to in a suitable way. The introduction of
quantum-group-covariant operators in the three dimensional picture gives a
generalisation of the quantum-group version of discrete three-dimensional
gravity that includes tetrahedra associated with 3-j symbols and universal
R-matrix elements. Altogether the present work gives the concrete realization
of Moore and Seiberg's scheme that describes the chiral operator-algebra of
two-dimensional gravity and minimal models.Comment: 56 pages, 22 figures. Technical problem only, due to the use of an
old version of uuencode that produces blank characters some times suppressed
by the mailer. Same content
Quantum Group Structure and Local Fields in the Algebraic Approach to 2D Gravity
This review contains a summary of work by J.-L. Gervais and the author on the
operator approach to 2d gravity. Special emphasis is placed on the construction
of local observables -the Liouville exponentials and the Liouville field itself
- and the underlying algebra of chiral vertex operators. The double quantum
group structure arising from the presence of two screening charges is discussed
and the generalized algebra and field operators are derived. In the last part,
we show that our construction gives rise to a natural definition of a quantum
tau function, which is a noncommutative version of the classical
group-theoretic representation of the Liouville fields by Leznov and Saveliev.Comment: 38 pages, LaTex file. Proceedings of the Vth International Conference
on Mathematical Physics, Strings and Quantum gravity, Alushta, Ukraine 199
Supersymmetric Black Holes from Toda Theories
On the example of nonabelian Toda type theory associated with the Lie
superalgebra we show that this integrable dynamical system is
relevant to a black hole background metric in the corresponding target space.
In the even sector the model under consideration reduces to the exactly
solvable conformal theory (nonabelian Toda system) in the presence of a
black hole recently proposed in the article "Black holes from non-abelian Toda
theories" by the last two authors (hep-th 9203039).Comment: 4 pages, Late
Lotka--Volterra Type Equations and their Explicit Integration
In the present note we give an explicit integration of some
two--dimensionalised Lotka--Volterra type equations associated with simple Lie
algebras, other than the familiar case, possessing a representation
without branching. This allows us, in particular, to treat the first
fundamental representations of , , , and on the same
footing.Comment: 3 pages LATEX fil
Strong-Coupling Effects in "Dirty" Superfluid
The contribution of the strong-coupling effects to the free energy of the
"dirty" superfluid is estimated using a simple model. It is shown that
the strong-coupling effects are less susceptible to the quasiparticle
scattering events in comparison to the weak-coupling counterpart. This supports
the conclusion about stabilization of the -phase in aerogel environment at
pressures where the -phase takes over in bulk superfluid , in
accordance with recent experimental observations in zero magnetic field.Comment: 10 pages, LaTeX file. This is a revised version of the paper with
some additional comments and references, and corrected typos. Submitted to
Journal of Physics: Condensed Matte
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