Spacetime symmetriesSpacetime symmetries are features of spacetime that can be described as exhibiting some form of symmetry. The role of symmetry in physics is important in simplifying solutions to many problems. Spacetime symmetries are used in the study of exact solutions of Einstein's field equations of general relativity. Spacetime symmetries are distinguished from internal symmetries. Physical problems are often investigated and solved by noticing features which have some form of symmetry.
Homological mirror symmetryHomological mirror symmetry is a mathematical conjecture made by Maxim Kontsevich. It seeks a systematic mathematical explanation for a phenomenon called mirror symmetry first observed by physicists studying string theory. In an address to the 1994 International Congress of Mathematicians in Zürich, speculated that mirror symmetry for a pair of Calabi–Yau manifolds X and Y could be explained as an equivalence of a constructed from the algebraic geometry of X (the of coherent sheaves on X) and another triangulated category constructed from the symplectic geometry of Y (the derived ).
Dualité TEn théorie des cordes et des supercordes la dualité T désigne une dualité particulière sous laquelle un (ou plusieurs) rayon de compactification est inversé. Considérons dans un premier temps le cas le plus simple de dualité T. Si on compactifie la théorie bosonique sur un cercle de rayon alors les états de vide de la théorie sont doublement quantifiés de la façon suivante: le nombre quantique indique que la corde associée (ou plus précisément son centre de masse) possède un moment dans la direction de compactification.
Ddbar lemmaIn complex geometry, the lemma (pronounced ddbar lemma) is a mathematical lemma about the de Rham cohomology class of a complex differential form. The -lemma is a result of Hodge theory and the Kähler identities on a compact Kähler manifold. Sometimes it is also known as the -lemma, due to the use of a related operator , with the relation between the two operators being and so .
K-stabilityIn mathematics, and especially differential and algebraic geometry, K-stability is an algebro-geometric stability condition, for complex manifolds and complex algebraic varieties. The notion of K-stability was first introduced by Gang Tian and reformulated more algebraically later by Simon Donaldson. The definition was inspired by a comparison to geometric invariant theory (GIT) stability. In the special case of Fano varieties, K-stability precisely characterises the existence of Kähler–Einstein metrics.
Théorème de Noether (physique)Le théorème de Noether exprime l'équivalence qui existe entre les lois de conservation et l'invariance du lagrangien d'un système par certaines transformations (appelées symétries) des coordonnées. Démontré en 1915 et publié en 1918 par la mathématicienne Emmy Noether à Göttingen, ce théorème fut qualifié par Albert Einstein de « monument de la pensée mathématique » dans une lettre envoyée à David Hilbert en vue de soutenir la carrière de la mathématicienne.
Modèle cycliqueDans les années 1930, des physiciens notables comme Albert Einstein et Richard Tolman, ont envisagé la possibilité d'un modèle cyclique de l'univers comme une alternative éternelle au modèle d'un univers en expansion. Toutefois, les travaux de Tolman en 1934 ont montré que ces idées semblaient échouer à cause du deuxième principe de la thermodynamique : celui-ci établit que l'entropie ne peut qu'augmenter dans un système fermé. Le concept d'univers cyclique moderne fut introduit par John Wheeler.
Moduli (physics)In quantum field theory, the term moduli (or more properly moduli fields) is sometimes used to refer to scalar fields whose potential energy function has continuous families of global minima. Such potential functions frequently occur in supersymmetric systems. The term "modulus" is borrowed from mathematics (or more specifically, moduli space is borrowed from algebraic geometry), where it is used synonymously with "parameter". The word moduli (Moduln in German) first appeared in 1857 in Bernhard Riemann's celebrated paper "Theorie der Abel'schen Functionen".
Algebraic quantum field theoryAlgebraic quantum field theory (AQFT) is an application to local quantum physics of C*-algebra theory. Also referred to as the Haag–Kastler axiomatic framework for quantum field theory, because it was introduced by . The axioms are stated in terms of an algebra given for every open set in Minkowski space, and mappings between those. Let be the set of all open and bounded subsets of Minkowski space. An algebraic quantum field theory is defined via a net of von Neumann algebras on a common Hilbert space satisfying the following axioms: Isotony: implies .
