2,229 research outputs found
Integrable extensions of the rational and trigonometric Calogero Moser potentials
We describe the -matrix structure associated with integrable extensions,
containing both one-body and two-body potentials, of the Calogero-Moser
-body systems. We construct non-linear, finite dimensional Poisson algebras
of observables. Their limit realize the infinite Lie algebras Sdiff in the trigonometric case and
Sdiff in the rational case. It is then isomorphic to the
algebra of observables constructed in the two-dimensional collective string
field theory.Comment: 15 pages; LaTeX; PAR LPTHE 93-23 Revised version including extensive
modifications in the demonstrations and the reference
Collective field theory of the matrix-vector model
We construct collective field theories associated with one-matrix plus
vector models. Such field theories describe the continuum limit of spin
Calogero Moser models. The invariant collective fields consist of a scalar
density coupled to a set of fields in the adjoint representation of .
Hermiticity conditions for the general quadratic Hamiltonians lead to a new
type of extended non-linear algebra of differential operators acting on the
Jacobian. It includes both Virasoro and (included in ) current algebras. A systematic construction of exact
eigenstates for the coupled field theory is given and exemplified.Comment: OLatex file, 20 pages, no figures. Misprints corrected, references
added; reformulation of the constraint algebra and additional Comments on its
structure; additional Comments on the structure of the continuum limit;
Nuclear Physics B, to appea
The Classical -Matrix for the Relativistic Ruijsenaars-Schneider System
We compute the classical -matrix for the relativistic generalization of
the Calogero-Moser model, or Ruijsenaars-Schneider model, at all values of the
speed-of-light parameter . We connect it with the non-relativistic
Calogero-Moser -matrix and the
sine-Gordon soliton limit.Comment: LaTeX file, no figures, 8 page
Classical R-matrix structure for the Calogero model
A classical R-matrix structure is described for the Lax representation of the
integrable n-particle chains of Calogero-Olshanetski-Perelo\-mov. This R-matrix
is dynamical, non antisymmetric and non-invertible. It immediately triggers the
integrability of the Type I, II and III potentials, and the algebraic
structures associated with the Type V potential.Comment: Latex file 9 page
Deformed Double Yangian Structures
Scaling limits when q tends to 1 of the elliptic vertex algebras A_qp(sl(N))
are defined for any N, extending the previously known case of N=2. They realise
deformed, centrally extended double Yangian structures DY_r(sl(N)). As in the
quantum affine algebras U_q(sl(N)), and quantum elliptic affine algebras
A_qp(sl(N)), these algebras contain subalgebras at critical values of the
central charge c=-N-Mr (M integer, 2r=ln p/ln q), which become Abelian when
c=-N or 2r=Nh for h integer. Poisson structures and quantum exchange relations
are derived for their abstract generators.Comment: 16 pages, LaTeX2e Document - packages amsfonts,amssymb,subeqnarra
Classification of the solutions of constant rational semi-dynamical reflection equations
We propose a classification of the solutions K to the semi-dynamical
reflection equation with constant rational structure matrices associated to
rational scalar Ruijsenaars-Schneider model. Four sets of solutions are
identified and simple analytic transformations generate all solutions from
these sets.Comment: 12 pages, no figure. Dedicated to Daniel Arnaudo
C^{(2)}_{N+1} Ruijsenaars-Schneider models
We define the notion of C^{(2)}_{N+1} Ruijsenaars-Schneider models and
construct their Lax formulation. They are obtained by a particular folding of
the A_{2N+1} systems. Their commuting Hamiltonians are linear combinations of
Koornwinder-van Diejen ``external fields'' Ruijsenaars-Schneider models, for
specific values of the exponential one-body couplings but with the most general
2 double-poles structure as opposed to the formerly studied BC_N case.
Extensions to the elliptic potentials are briefly discussed.Comment: 15 pages, LaTeX, no figure
String field actions from W-infinity
Starting from as a fundamental symmetry and using the coadjoint
orbit method, we derive an action for one dimensional strings. It is shown that
on the simplest nontrivial orbit this gives the single scalar collective field
theory. On higher orbits one finds generalized KdV type field theories with
increasing number of components. Here the tachyon is coupled to higher tensor
fields.Comment: 18 page
Commuting quantum traces: the case of reflection algebras
We formulate a systematic construction of commuting quantum traces for
reflection algebras. This is achieved by introducing two sets of generalized
reflection equations with associated consistent fusion procedures. Products of
their solutions yield commuting quantum traces.Comment: 16 pages, Late
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