Olivier Babelon

Extended conformal algebra and the Yang-Baxter equation

Abstract Working in the context of classical Toda field theory, we derive their extended conformal symmetry algebra from their integrability properties.

Universal exchange algebra for Bloch waves and Liouville theory

We derive a universal formula for the exchange algebra in the Bloch wave basis. The main tool we use is a lattice version of the Coulomb gas picture of conformal field theory, making its quantum group structure explicit from the very beginning. Calulations are then reduced to a factorization problem inUq(sl2).

Introduction to Classical Integrable Systems: Frontmatter

published by the press syndicate of the university of cambridge

Introduction to Classical Integrable Systems: Contents

published by the press syndicate of the university of cambridge

The riemannian geometry of the configuration space of gauge theories

We state some new results about the configuration space of pure Yang-Mills theory. These results come from the study of the kinetic energy term of the Lagrangian of the theory. This term defines a riemannian metric on the space of non-equivalent gauge potentials. We develop a riemannian calculus on the configuration space, compute the riemannian connection, the curvature tensor, and solve for the geodesics, etc. We show that the Gribov ambiguity is more than an artefact of the choice of a gauge condition, and is related to the existence of conjugate points on the geodesics, and is thus an intrinsic feature of the theory.

Conformal affine sl2 toda field theory

Abstract We present a model based on the sl 2 affine algebra, which is integrable and conformally invariant. It reduces to the standard Liouville theory or to the sinh-Gordon model under certain limiting conditions. We find the general classical solution of this model and the exchange algebra.

The sine-Gordon solitons as an N-body problem

Abstract We consider the N -soliton solutions in the sine-Gordon model as an N -body problem. This leads to a relativistic generalization of the Calogero model first introduced by Ruijsenaars. We show that the fundamental Poisson bracket of the Lax matrix is quadratic, and the r -matrix is a dynamical one. This is in contrast to the Calogero model where the fundamental Poisson bracket of the Lax matrix is linear.

The geometrical interpretation of the Faddeev-Popov determinant

Abstract We give a geometrical interpretation of the Faddeev-Popov determinant in Yang-Mills theories by comparing it to the natural metric on the orbit space.

Exchange formula and lattice deformation of the Virasoro algebra

Abstract We show that the exchange formula can be used to define an integrable discretization of conformal field theory.

From form factors to correlation functions. The Ising model

Abstract Using exact expressions for the Ising form factors, we give a new very simple proof that the spin-spin and disorder-disorder correlation functions are governed by the Painleve III nonlinear differential equation. We also snow that the generating function of the correlation functions of the descendents of the spin and disorder operators is an N -soliton, N → ∞, τ-funtion of the sinh-Gordon hierarchy. We discuss a relation of our approach to isomonodromy deformation problems, as well as further possible generalizations.