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Science/Engineering Yang-Mills, Kaluza-Klein, and the Einstein Program (Interdisciplinary Mathematics ; V. 19)
Posted on 2010-03-16
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More Yang-Mills, Kaluza-Klein, and the Einstein Program (Interdisciplinary Mathematics ; V. 19): Robert Hermann The main new material in this volume concerns old wine in new bottles. As I have been emphasizing in my work, gauge fields are precisely what we call connections. Now, as mathematics, this subject was very well developed and understood when I became a graduate student in 1952... My point in this book is that the ``Yang-Mills" idea can be traced back even further to the Kaluza-Klein ``unified field theory" of the early 1920's. Of course, then it was a question of unifying gravitation and electromagnetics. The Yang-Mills fields are a direct generalization of the electromagnetic field and it should not be surprising that the Kaluza-Klein construction generalizes. The message of my work here is that it does, and that it involves precisely the notion of a connection on a principal fiber bundle. There are also implications for the ``generalized Aharanov-Bohm" situation, recently considered by Wu and Yang. Download Link (Uploading.com) To see my other books, click Download Link (Here). "
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