Titlebook: Geometric Analysis and Applications to Quantum Field Theory; Peter Bouwknegt,Siye Wu Textbook 2002 Springer Science+Business Media New Yor

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,The Knizhnik—Zamolodchikov Equations,ol on “Differential Equations in Geometry and Physics.” This article does not constitute a comprehensive account of all that is known about the KZ equations but, rather, is an introduction to some of the main results intended to motivate the reader to further study. The three main sections can be re

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Loop Groups and Quantum Fields,stems. The common thread in the discussion is the construction of quantum fields using vertex operators. These examples include the construction and solution of the Luttinger model and other 1+1 dimensional interacting quantum field theories, the construction of anyon field operators on the circle,

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,Gromov—Witten Invariants and Quantum Cohomology,mplectic manifolds as intersection pairings on the moduli space of pseudoholomorphic curves. The invariants are computed in various examples. We also study the quantum product structure on the cohomology groups and its associativity. In Section 2, we introduce relative Gromov—Witten invariants when

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,The Geometry and Physics of the Seiberg—Witten Equations, the exposition, we will cover several rich aspects of nonperturbative quantum field theory. Attempts have been made to reduce the prerequisites to a minimum and to provide a comprehensive bibliography. Lecture 1 explains classical and quantum pure gauge theory and its supersymmetric versions, with

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Geometric Analysis and Applications to Quantum Field Theory978-1-4612-0067-3Series ISSN 0743-1643 Series E-ISSN 2296-505X

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https://doi.org/10.1007/978-981-15-1318-3Monopoles are solutions of the Bogomolny equation in ℝ.. They are introduced and an overview is given of various approaches to studying and understanding them: spectral curves, holomorphic bundles on mini-twistor space, Nahm’s equations and rational maps.

Prognosis

Monopoles,Monopoles are solutions of the Bogomolny equation in ℝ.. They are introduced and an overview is given of various approaches to studying and understanding them: spectral curves, holomorphic bundles on mini-twistor space, Nahm’s equations and rational maps.