This e-book presents an advent to noncommutative geometry and provides a few its fresh functions to particle physics. it's meant for graduate scholars in mathematics/theoretical physics who're new to the sector of noncommutative geometry, in addition to for researchers in mathematics/theoretical physics with an curiosity within the actual functions of noncommutative geometry. within the first half, we introduce the most innovations and strategies via learning finite noncommutative areas, delivering a “light” method of noncommutative geometry. We then continue with the overall framework by means of defining and interpreting noncommutative spin manifolds and deriving a few major effects on them, resembling the neighborhood index formulation. within the moment half, we express how noncommutative spin manifolds obviously supply upward push to gauge theories, making use of this precept to precise examples. We for this reason geometrically derive abelian and non-abelian Yang-Mills gauge theories, and at last the whole general version of particle physics, and finish by means of explaining how noncommutative geometry may possibly point out find out how to continue past the traditional version.
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