18 research outputs found
R-Matrix Formulation of KP Hierarchies and their Gauge Equivalence
The Adler-Kostant-Symes -bracket scheme is applied to the algebra of
pseudo-differential operators to relate the three integrable hierarchies: KP
and its two modifications, known as nonstandard integrable models. All three
hierarchies are shown to be equivalent and connection is established in the
form of a symplectic gauge transformation. This construction results in a new
representation of the W-infinity algebras in terms of 4 bosonic fields.Comment: 13 pages, Latex, CERN-TH.6627/9
Integrable Perturbations of and WZW Models
We present a new class of 2d integrable models obtained as perturbations of
minimal CFT with W-symmetry by fundamental weight primaries. These models are
generalisations of well known -perturbed Virasoro minimal models. In the
large (number of minimal model) limit they coincide with scalar
perturbations of WZW theories. The algebra of conserved charges is discussed in
this limit. We prove that it is noncommutative and coincides with twisted
affine algebra represented in a space of asymptotic states. We conjecture
that scattering in these models for generic is described by -matrix of
the -deformed - algebra with being root of unity.Comment: 10p., LaTeX, preprint SISSA 19/94/FM (references added
Induced Gravity as a WZNW Model
We derive the explicit form of the Wess-Zumino quantum effective action of
chiral \Winf-symmetric system of matter fields coupled to a general chiral
\Winf-gravity background. It is expressed as a geometric action on a
coadjoint orbit of the deformed group of area-preserving diffeomorphisms on
cylinder whose underlying Lie algebra is the centrally-extended algebra of
symbols of differential operators on the circle. Also, we present a systematic
derivation, in terms of symbols, of the "hidden" SL(\infty;\IR) Kac-Moody
currents and the associated SL(\infty;\IR) Sugawara form of energy-momentum
tensor component as a consequence of the SL(\infty;\IR) stationary
subgroup of the relevant \Winf coadjoint orbit
Classification of Quantum Hall Universality Classes by $\ W_{1+\infty}\ $ symmetry
We show how two-dimensional incompressible quantum fluids and their
excitations can be viewed as edge conformal field theories,
thereby providing an algebraic characterization of incompressibility. The
Kac-Radul representation theory of the algebra leads then to
a purely algebraic complete classification of hierarchical quantum Hall states,
which encompasses all measured fractions. Spin-polarized electrons in
single-layer devices can only have Abelian anyon excitations.Comment: 11 pages, RevTeX 3.0, MPI-Ph/93-75 DFTT 65/9
Sigma models as perturbed conformal field theories
We show that two-dimensional sigma models are equivalent to certain perturbed
conformal field theories. When the fields in the sigma model take values in a
space G/H for a group G and a maximal subgroup H, the corresponding conformal
field theory is the limit of the coset model , and the
perturbation is related to the current of G. This correspondence allows us for
example to find the free energy for the "O(n)" (=O(n)/O(n-1)) sigma model at
non-zero temperature. It also results in a new approach to the CP^{n} model.Comment: 4 pages. v2: corrects typos (including several in the published
version
Time Dynamics of Probability Measure and Hedging of Derivatives
We analyse derivative securities whose value is NOT a deterministic function of an underlying which means presence of a basis risk at any time. The key object of our analysis is conditional probability distribution at a given underlying value and moment of time. We consider time evolution of this probability distribution for an arbitrary hedging strategy (dynamically changing position in the underlying asset). We assume log-brownian walk of the underlying and use convolution formula to relate conditional probability distribution at any two successive time moments. It leads to the simple PDE on the probability measure parametrized by a hedging strategy. For delta-like distributions and risk-neutral hedging this equation reduces to the Black-Scholes one. We further analyse the PDE and derive formulae for hedging strategies targeting various objectives, such as minimizing variance or optimizing quantile position.