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Il peut sembler à première vue surprenant de rechercher chez un auteur disparu il y a trois siècles des précisions ou des distinctions pertinentes pour clarifier les enjeux et les formulations des discussions contemporaines portant sur la notion de disposition. Qu’il s’agisse des concepts, des méthodes ou de l'état des connaissances, nous sommes en effet plutôt enclins à voir dans l’univers que décrit la philosophie leibnizienne un ensemble de conceptions relativement étrangères aux questions...

Philosophy --- Leibniz --- dispositions --- causalité --- puissance --- mécanique --- mécanique quantique

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En suivant deux fils rouges, l’histoire des grandes révolutions de la physique au xxe siècle et l’abstraction progressive du concept de symétrie, de son usage ordinaire en géométrie à son application aux lois de la physique, cette leçon inaugurale aborde un des défis majeurs de la physique actuelle, celui de réconcilier la relativité d'Einstein et la mécanique quantique, théories amplement vérifiées empiriquement et pourtant incompatibles. C’est peut-être dans une symétrie immense, décrite en théorie des groupes par des groupes très particuliers, que réside la clé pour formuler cette théorie plus fondamentale de la gravitation, qui pourrait permettre la grande synthèse avec la mécanique quantique.

Multidisciplinary --- physique --- mécanique quantique --- relativité --- gravitation --- symétrie --- Big Bang --- théorie des cordes --- théorie des groupes --- Physics --- Gravity --- Quantum physics (quantum mechanics & quantum field theory) --- Relativity physics

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This monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structure—the Schrödinger-Virasoro algebra. Just as Poincaré invariance or conformal (Virasoro) invariance play a key role in understanding, respectively, elementary particles and two-dimensional equilibrium statistical physics, this algebra of non-relativistic conformal symmetries may be expected to apply itself naturally to the study of some models of non-equilibrium statistical physics, or more specifically in the context of recent developments related to the non-relativistic AdS/CFT correspondence.   The study of the structure of this infinite-dimensional Lie algebra touches upon topics as various as statistical physics, vertex algebras, Poisson geometry, integrable systems and supergeometry as well as representation theory, the cohomology of infinite-dimensional Lie algebras, and the spectral theory of Schrödinger operators. .

Schrödinger equation. --- Algebra. --- Schrödinger operator. --- Operator, Schrödinger --- Differential operators --- Quantum theory --- Schrödinger equation --- Mathematics --- Mathematical analysis --- Equation, Schrödinger --- Schrödinger wave equation --- Differential equations, Partial --- Particles (Nuclear physics) --- Wave mechanics --- WKB approximation --- Representations of Lie algebras. --- Infinite dimensional Lie algebras. --- Mathematical physics. --- Topological Groups. --- Statistical physics. --- Mathematical Methods in Physics. --- Topological Groups, Lie Groups. --- Mathematical Physics. --- Category Theory, Homological Algebra. --- Complex Systems. --- Statistical Physics and Dynamical Systems. --- Physics --- Mathematical statistics --- Groups, Topological --- Continuous groups --- Physical mathematics --- Statistical methods --- Physics. --- Topological groups. --- Lie groups. --- Category theory (Mathematics). --- Homological algebra. --- Dynamical systems. --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Homological algebra --- Algebra, Abstract --- Homology theory --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Lie, Algèbres de --- Représentations d'algèbres de Lie --- Representations of Lie algebras --- Lie, Algèbres de --- Lie algebras. --- Représentations d'algèbres de Lie. --- Mecanique quantique --- Application de la theorie des groupes --- Schrodinger equation. --- Schrodinger operator.