Item description for Geometry, Topology and Physics: Proceedings of the First Brazil-USA Workshop Held in Campinas, Brazil, June 30-July 7, 1996 by B. N. Apanasov, B. N. Apanasov & Brazil) Brazil-USA Workshop 1996 (Campinas...
Geometry, Topology and Physics: Proceedings of the First Brazil-USA Workshop Held in Campinas, Brazil, June 30-July 7, 1996 by B. N. Apanasov Brazil) Brazil-USA Workshop 1996 (Campinas
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Est. Packaging Dimensions: Length: 1" Width: 7" Height: 9.75" Weight: 1.65 lbs.
Publisher Walter de Gruyter
ISBN 311015594X ISBN13 9783110155945
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Apanasov et al's Geometry, Topology, and Physics Apr 18, 2000
The rapidly rising Brazilian, Mexican, and other Latin American schools in mathematics and physics are contributors to this remarkable volume published by Walter de Gruyter: Berlin. I will concentrate here on the article by J. Vaz, Jr., one of the world's greatest mathematicians and physicists. In the following, I assume that the reader who is not a specialist in this area will hire a reputable consultant or tutor to translate the book into approximately ordinary English or elementary math/physics, since the book gives valuable lessons for almost every field of interest. Vaz's paper is "Clifford algebra's and Witten's Monopole Equations." See my reviews of Chisholm, Okubo, Benn, Baylis, Kursunoglu, and others on monopoles and Clifford algebras for some simple explanations. E. Witten is with the Institute for Advanced Study at Princeton. It turns out that GUTs (Grand Unified Theories of the Elementary Forces and Particles) predict the existence of monopoles, which have the remarkable property of being either north or south poles but not both, unlike all magnets that we are familiar with in daily life. Dirac and then t'Hooft have come up with basic monopole equations, and now Witten has also, and Vaz analyzes these using Clifford algebras. He reformulates Witten's equations in Maxwell equation form using the idea of operator spinors, and then obtains a representation without spinors and another representation with an SU(2) connection related to the spinor connection with values in the Lie algebra of SU(2). An important theorem, the inversion theorem, is a major tool used by Vaz. The final reformulation involves the spinor covariant derivative acting on spinors. Lie algebras are so remarkable that I will try to give some simple definitions for them in subsequent reviews of books on Lie algebras.