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Monopole Moduli Space
In mathematics, the monopole moduli space is a space parametrizing monopoles (solutions of the Bogomolny equations). studied the moduli space for 2 monopoles in detail and used it to describe the scattering of monopoles. See also * Hitchin system References *{{Citation , last1=Atiyah , first1=Michael , author1-link=Michael Atiyah , author2-link=Nigel Hitchin , last2=Hitchin , first2=Nigel , title=The geometry and dynamics of magnetic monopoles , publisher=Princeton University Press Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial su ... , series=M. B. Porter Lectures , isbn=978-0-691-08480-0 , mr=934202 , year=1988 Differential geometry ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bogomolny Equations
In mathematics, and especially gauge theory, the Bogomolny equation for magnetic monopoles is the equation :F_A = \star d_A \Phi, where F_A is the curvature of a connection A on a principal G-bundle over a 3-manifold M, \Phi is a section of the corresponding adjoint bundle, d_A is the exterior covariant derivative induced by A on the adjoint bundle, and \star is the Hodge star operator on M. These equations are named after E. B. Bogomolny and were studied extensively by Michael Atiyah and Nigel Hitchin. The equations are a dimensional reduction of the self-dual Yang–Mills equations from four dimensions to three dimensions, and correspond to global minima of the appropriate action. If M is closed, there are only trivial (i.e. flat) solutions. See also * Monopole moduli space *Ginzburg–Landau theory *Seiberg–Witten theory *Bogomol'nyi–Prasad–Sommerfield bound The Bogomol'nyi–Prasad–Sommerfield bound (named after Evgeny Bogomolny, M.K. Prasad, and Charle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moduli Space
In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. Such spaces frequently arise as solutions to classification problems: If one can show that a collection of interesting objects (e.g., the smooth algebraic curves of a fixed genus) can be given the structure of a geometric space, then one can parametrize such objects by introducing coordinates on the resulting space. In this context, the term "modulus" is used synonymously with "parameter"; moduli spaces were first understood as spaces of parameters rather than as spaces of objects. A variant of moduli spaces is formal moduli. Motivation Moduli spaces are spaces of solutions of geometric classification problems. That is, the points of a moduli space correspond to solutions of geometric problems. Here different solutions are identified if they a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hitchin System
In mathematics, the Hitchin integrable system is an integrable system depending on the choice of a complex reductive group and a compact Riemann surface, introduced by Nigel Hitchin in 1987. It lies on the crossroads of algebraic geometry, the theory of Lie algebras and integrable system theory. It also plays an important role in the geometric Langlands correspondence over the field of complex numbers through conformal field theory. A genus zero analogue of the Hitchin system, the Garnier system, was discovered by René Garnier somewhat earlier as a certain limit of the Schlesinger equations, and Garnier solved his system by defining spectral curves. (The Garnier system is the classical limit of the Gaudin model. In turn, the Schlesinger equations are the classical limit of the Knizhnik–Zamolodchikov equations). Almost all integrable systems of classical mechanics can be obtained as particular cases of the Hitchin system or their common generalization defined by Bottacin and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial support of Charles Scribner, as a printing press to serve the Princeton community in 1905. Its distinctive building was constructed in 1911 on William Street in Princeton. Its first book was a new 1912 edition of John Witherspoon's ''Lectures on Moral Philosophy.'' History Princeton University Press was founded in 1905 by a recent Princeton graduate, Whitney Darrow, with financial support from another Princetonian, Charles Scribner II. Darrow and Scribner purchased the equipment and assumed the operations of two already existing local publishers, that of the ''Princeton Alumni Weekly'' and the Princeton Press. The new press printed both local newspapers, university documents, ''The Daily Princetonian'', and later added book publishing to it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |