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12 pages, 2009 preprint

Abstract:

One of the great mathematicians and mathematical physicists of the 20th century, E'lie Cartan worked intensely on the group of rotations in n-dimensional Euclidean spaces and spinors in three-dimensional space. In his fundamental book on the theory of spinors ("The Theory of Spinors", 1966 by Hermann, Paris) in n-dimensional Euclidean spaces, and also in the special relativity Minkowski space, he developed all the fundamental concepts in a mathematically rigorous manner. The final chapters of his spinor book focused on the connection between the spinors and the Lorentz group of transformations, including also in a later section connections with Einstein's general relativity theory. However, it concluded disappointingly that fields of spinors cannot be "introduced into the classical Riemannian technique". The spinor theory is re-considered in the light of QFT and QED theories in modern quantum physics, and still draws substantial attention from mathematicians. http://arxiv.org/pdf/hep-th/0012203 http://www.emis.de/newsletter/newsletter36.pdf http://www.sciencetimeline.net/bibliography.htm

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