Search results for " 53-02"
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Deformation Quantization: Genesis, Developments and Metamorphoses
2002
We start with a short exposition of developments in physics and mathematics that preceded, formed the basis for, or accompanied, the birth of deformation quantization in the seventies. We indicate how the latter is at least a viable alternative, autonomous and conceptually more satisfactory, to conventional quantum mechanics and mention related questions, including covariance and star representations of Lie groups. We sketch Fedosov's geometric presentation, based on ideas coming from index theorems, which provided a beautiful frame for developing existence and classification of star-products on symplectic manifolds. We present Kontsevich's formality, a major metamorphosis of deformation qu…
La théorie des lignes parallèles de Johann Heinrich Lambert
2014
International audience; The memoir "Theory of parallel lines" (1766) by Johannes Heinrich Lambert is one of the founding texts of hyperbolic geometry, even though his author conceived it as an attempt to show that this geometry does not exist. In fact, Lambert developed that theory with the hope of finding a contradiction. In doing so, he obtained several fundamental results of hyperbolic geometry. This was sixty years before the first writings of Lobachevsky and Bolyai appeared in print. This book contains the first complete translation of Lambert's memoir as well as mathematical and historical commentaries.