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In 1993, M. Kontsevich proposed a conceptual framework for explaining the phenomenon of mirror symmetry. Mirror symmetry had been discovered by physicists in string theory as a duality between families of three-dimensional Calabi–Yau manifolds. Kontsevich's proposal uses Fukaya's construction of the A∞-category of Lagrangian submanifolds on the symplectic side and the derived category of coherent sheaves on the complex side. The theory of mirror symmetry was further enhanced by physicists in the language of D-branes and also by Strominger–Yau–Zaslow in the geometric set-up of (special) Lagrangian torus fibrations. It rapidly expanded its scope across from geometry, topology, algebra to physics. In this volume, leading experts in the field explore recent developments in relation to homological mirror symmetry, Floer theory, D-branes and Gromov–Witten invariants. Kontsevich-Soibelman describe their solution to the mirror conjecture on the abelian variety based on the deformation theory of A∞-categories, and Ohta describes recent work on the Lagrangian intersection Floer theory by Fukaya–Oh–Ohta–Ono which takes an important step towards a rigorous construction of the A∞-category. There follow a number of contributions on the homological mirror symmetry, D-branes and the Gromov–Witten invariants, e.g. Getzler shows how the Toda conjecture follows from recent work of Givental, Okounkov and Pandharipande. This volume provides a timely presentation of the important developments of recent years in this rapidly growing field.
Mirror symmetry --- Symplectic groups --- Groups, Symplectic --- Linear algebraic groups --- Symmetry (Physics)
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Solid state physics --- Molecules --- Symmetry (Physics) --- Lattice theory
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This collection of papers provides a broad view of the development of Lorentz and Poincaré invariance and space time symmetry throughout the past 100 years. The issues explored in these papers include: (1) formulations of relativity theories in which the speed of light is not a universal constant but which are consistent with the four-dimensional symmetry of the Lorentz and Poincaré groups and with experimental results, (2) analyses and discussions by Reichenbach concerning the concepts of simultaneity and physical time from a philosophical point of view, and (3) results achieved by the union
Symmetry (Physics) --- Relativity (Physics) --- Gravitation --- Nonrelativistic quantum mechanics --- Space and time --- Invariance principles (Physics) --- Symmetry (Chemistry) --- Conservation laws (Physics) --- Physics
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This is a pedagogical introduction to the harmonic superspace method in extended supersymmetry. Inspired by exciting developments in superstring theory, it provides a systematic treatment of the quantum field theories with N=2 and N=3 supersymmetry in harmonic superspace. The authors present the harmonic superspace approach as a means of providing an off-shell description of the N=2 supersymmetric theories, both at the classical and quantum levels. Furthermore, they show how it offers a unique way to construct an off-shell formulation of a theory with higher supersymmetry, namely the N=3 supersymmetric Yang-Mills theory. Harmonic Superspace makes manifest many remarkable geometric properties of the N=2 theories, for example, the one-to-one correspondence between N=2 supersymmetric matter, and hyper-Kähler and quaternionic manifolds. This book will be of interest to researchers and graduate students working in the areas of supersymmetric quantum field theory, string theory and complex geometries.
Supersymmetry. --- Unified theories --- Particles (Nuclear physics) --- Symmetry (Physics) --- Supersymmetry --- Supersymétrie
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The third conference on "Symmetry and Perturbation Theory" (SPT2001) was attended by over 50 mathematicians, physicists and chemists. The proceedings present the advancement of research in this field - more precisely, in the different fields at whose crossroads symmetry and perturbation theory sit.
Contents:
Symmetry (Physics) --- Perturbation (Mathematics) --- Perturbation equations --- Perturbation theory --- Approximation theory --- Dynamics --- Functional analysis --- Mathematical physics
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Aesthetics --- Esthetica --- Esthétique --- Aesthetics. --- Beautiful, The --- Beauty --- Esthetics --- Taste (Aesthetics) --- Philosophy --- Art --- Criticism --- Literature --- Proportion --- Symmetry --- Psychology --- Radio broadcasting Aesthetics
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Aesthetics. --- Aesthetics --- Beautiful, The --- Beauty --- Esthetics --- Taste (Aesthetics) --- Philosophy --- Art --- Criticism --- Literature --- Proportion --- Symmetry --- Psychology --- Radio broadcasting Aesthetics
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In chapters ranging from "The Beautiful, the Dainty, and the Dumpy" to "Skin-deep or In the Eye of the Beholder?" Nick Zangwill investigates the nature of beauty as we conceive it, and as it is in itself. The notion of beauty is currently attracting increased interest, particularly in philosophical aesthetics and in discussions of our experiences and judgments about art. In The Metaphysics of Beauty, Zangwill argues that it is essential to beauty that it depends on the ordinary features of things. He uses this principle to defend the notion of the aesthetic, to call for a version of aesthetic formalism, and to reconsider the reality of beauty. The Metaphysics of Beauty brings beauty to the center of intellectual consciousness in a manner informed by contemporary metaphysics and engages with beauty as an enduring object of human thought and experience.
Aesthetics. --- Beautiful, The --- Beauty --- Esthetics --- Taste (Aesthetics) --- Philosophy --- Art --- Criticism --- Literature --- Proportion --- Symmetry --- Psychology --- Radio broadcasting Aesthetics --- Aesthetics
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