Michel Talon

Classical R matrix structure for the Calogero model

Abstract A classical R-matrix structure is described for the Lax representation of the integrable n-particle chains of Calogero, Olshanetski and Perelomov. 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.

{BRS} Algebras: Analysis of the Consistency Equations in Gauge Theory

We compute all possible anomalous terms in quantum gauge theory in the natural class of polynomials of differential forms. By using the appropriate cohomological and algebraic methods, we do it for all dimensions of spacetime and all structure groups with reductive Lie algebras.

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

General solution of the consistency equation

Abstract We produce the general solution of the Wess-Zumino consistency condition for gauge theories of the Yang-Mills type, for any ghost number and form degree. We resolve the problem of the cohomological independence of these solutions. In other words we fully describe the local version of the cohomology of the BRS operator, modulo the differential on space-time. This in particular includes the presence of external fields and non-trivial topologies of space-time.

Some results on local cohomologies in field theory

Abstract We prove that the local cohomology of the exterior differential is trivial. This is done through homotopy and spectral sequence arguments. We then give relations between various cohomologies (especially cohomologies of one differential modulo another one). Using these results we give a direct proof of the locality of the gauge fixed action in the BRST formalism.

Results on BRS cohomologies in gauge theory

Abstract We compute the cohomology of the Becchi-Rouet-Stora operator in gauge theory over general space-time M without boundary, with structure group G, for class of polynomial functions of the field. We show that the problem reduces to a standard problem for the finite dimensional group G. As a consequence, we prove that, within this class of polynomials, all anomalies and Schwinger terms are obtained from invariants of G.

The Adler-van Moerbeke model. Lax representation and poisson structure☆

Abstract We study the classical integrability of the Adler-van Moerbeke model, describing in particular cases the motion on an ellipsoid with a central force. Classical integrability is associated with a generalized structure for the Poisson brackets of the Lax operator. The already known set of conserved quantities for this model turns out to follow straightforwardly from this structure.