Modern Differential Geometry in Gauge Theories (Progress in by Anastasios Mallios

By Anastasios Mallios

Differential geometry, within the classical experience, is built during the conception of tender manifolds. sleek differential geometry from the author’s point of view is utilized in this paintings to explain actual theories of a geometrical personality with no utilizing any inspiration of calculus (smoothness). as an alternative, an axiomatic remedy of differential geometry is gifted through sheaf concept (geometry) and sheaf cohomology (analysis). utilizing vector sheaves, rather than bundles, in accordance with arbitrary topological areas, this new angle often furthers new views and calculations that generate unforeseen strength purposes. glossy Differential Geometry in Gauge Theories is a two-volume study monograph that systematically applies a sheaf-theoretic method of such actual theories as gauge idea. starting with quantity 1, the point of interest is on Maxwell fields. carrying on with in quantity 2, this sheaf-theoretic procedure is utilized to Yang–Mills fields quite often. The textual content includes a wealth of particular and rigorous computations and may entice mathematicians and physicists, besides complicated undergraduate and graduate scholars, attracted to functions of differential geometry to actual theories reminiscent of normal relativity, uncomplicated particle physics and quantum gravity.

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