Michel Talon

Solitons et systèmes intégrables

Mathématiques, 2015

Le terme soliton vient de l'observation par John Scott Russell, communiquee a la Royal Societ... more Le terme soliton vient de l'observation par John Scott Russell, communiquee a la Royal Society d'Edimbourgh en 1834, de ce qu'il a appele a l'epoque une « onde solitaire » (solitary wave): une vague s'est formee a la proue d'une barge et a continue sa course pendant plus d'un kilometre, sans deformation, avec une vitesse relativement importante et constante. Le phenomene est similaire au mascaret et aux raz de maree. Sa comprehension, et sa description par une equation, s'est faite tres progressivement. Nous presenterons autant que possible la modelisation par des equations plutot que la description superficielle du phenomene. La theorie lineaire de la propagation d'ondes a la surface de l'eau, qui contient des termes dispersifs, n'explique pas la propagation sans deformation de l'onde solitaire. Cette onde devrait s'etaler et disparaitre et il a ete necessaire de donner une autre description mathematique.

Перенормировка волновой функции для связанных частиц

Nuovo Cimento Della Societa Italiana Di Fisica A-nuclei Particles and Fields, 1983

Summary Formulae are given for conventional wave function renormalization of coupled systems of ... more

Радиационный, иэменяюший аромат, распад нейтрального тока

Nuovo Cimento Della Societa Italiana Di Fisica A-nuclei Particles and Fields, 1984

Summary We compute the (flavour-changing) decays of the neutral current induced by radiative cor... more

Some results on local cohomologies in field theory

Physics Letters B, 1991

We prove that the local cohomology of the exterior differential is trivial. This is done through ... more

The quantum Neumann model: refined semiclassical results

We extend the semiclassical study of the Neumann model down to the deep quantum regime. A detaile... more

format_quoteStates become delocalized with shrinking sphere radius, lifting degeneracy by a finite quantity, relevant at the zero radius limit.format_quote

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Poisson Structure and Integrability of the Neumann-Moser-Uhlenbeck Model

International Journal of Modern Physics A, 1990

Neumann’s model, describing the motion of a particle on an N-sphere under harmonic forces, is stu... more Neumann’s model, describing the motion of a particle on an N-sphere under harmonic forces, is studied from the point of view of classical and quantum integrability. Classical integrability is derived from a generalized structure, “R-S couple” or “D-matrix” 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. It gives rise to a set of commuting operators at the quantum level, and the algebra of Lax operators directly follows from the classical one.

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

We study the classical integrability of the Adler-van Moerbeke model, describing in particular ca... more 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.

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The quantum Neumann model: asymptotic analysis

Physics Letters A, 2006

In a previous publication [1], we have explained how to determine numerically the spectrum of the... more

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BRS algebras. Analysis of the consistency equations in gauge theory

… in Mathematical Physics, 1985

M. Dubois-Violette 1, M. Talon z, and CM Viallet 2 1 Laboratoire de Physique Th6orique et Hautes ... more

The quantum Neumann model: asymptotic analysis

We use semi–classical and perturbation methods to establish the quantum theory of the Neumann mod... more

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The quantum Neumann model: refined semiclassical results

We extend the semiclassical study of the Neumann model down to the deep quantum regime. A detaile... more

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Introduction to classical integrable systems

1. Introduction 2. Integrable dynamical systems 3. Synopsis of integrable systems 4. Algebraic me... more 1. Introduction 2. Integrable dynamical systems 3. Synopsis of integrable systems 4. Algebraic methods 5. Analytical methods 6. The closed Toda chain 7. The Calogero-Moser model 8. Isomonodromic deformations 9. Grassmannian and integrable hierarchies 10. The KP hierarchy 11. The KdV hierarchy 12. The Toda field theories 13. Classical inverse scattering method 14. Symplectic geometry 15. Riemann surfaces 16. Lie algebras Index.

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Quantum theory for the Standard Model

arXiv: High Energy Physics - Phenomenology, 1993

These lectures present some basic facts in field theory necessary to understand the quantum theor... more

format_quoteFeynman propagator derived from harmonic oscillator analysis confirms the correct boundary conditions without Euclidean region.format_quote

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Spectrum of the quantum Neumann model

We study numerically the spectrum and eigenfunctions of the quantum Neumann model, illustrating s... more

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Introduction to classical integrable systems

This book provides a thorough introduction to the theory of classical integrable systems, discuss... more

Weak radiative corrections to biphotonic pair annihilations

Nuclear Physics B, 1985

Neutral and charged current radiative corrections to e+e-+ yy are computed in the Weinberg-Salam ... more Neutral and charged current radiative corrections to e+e-+ yy are computed in the Weinberg-Salam model. It is found that the charged current dominates the result and induces a-1% percentage correction, neatly characterized by polarization effects. So e+e-+ yy provides a clean test for weak radiative corrections.

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Weak radiative corrections to e+e−→γZ

Il Nuovo Cimento A, 1985

Summary We compute fourth-order weak radiative corrections to the e+e− → γZ process in the Weinb... more

Radiative flavour-changing decay of the neutral current

Il Nuovo Cimento A, 1984

Weak radiative corrections at LEP

Annales de Physique, 1988

Weak radiative corrections in the Weinberg-Salam model are reviewed, in the perspective of new re... more Weak radiative corrections in the Weinberg-Salam model are reviewed, in the perspective of new results at LEP. They should be identified with good precision. This would settle Weinberg-Salam model position among various possible extensions. Les corrections radiatives faibles au modèle de Weinberg et Salam sont passées en revue dans la perspective des expériences et résultats que l&amp;amp;#39;on pourra obtenir au

BRS algebras. Analysis of the consistency equations in gauge theory

Communications in Mathematical Physics, 1985

M. Dubois-Violette 1, M. Talon z, and CM Viallet 2 1 Laboratoire de Physique Th6orique et Hautes ... more

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