By George A. Anastassiou, Visit Amazon's Anastasios Mallios Page, search results, Learn about Author Central, Anastasios Mallios,
Differential geometry, within the classical experience, is constructed during the idea of soft 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 out utilizing any suggestion of calculus (smoothness). in its place, an axiomatic therapy of differential geometry is gifted through sheaf idea (geometry) and sheaf cohomology (analysis). utilizing vector sheaves, instead of bundles, in keeping with arbitrary topological areas, this special approach quite often furthers new perspectives and calculations that generate unforeseen power applications.
Modern Differential Geometry in Gauge Theories is a two-volume examine monograph that systematically applies a sheaf-theoretic method of such actual theories as gauge thought. starting with quantity 1, the point of interest is on Maxwell fields. the entire simple thoughts of this mathematical process are formulated and used thereafter to explain straightforward debris, electromagnetism, and geometric prequantization. Maxwell fields are totally tested and labeled within the language of sheaf concept and sheaf cohomology. carrying on with in quantity 2, this sheaf-theoretic process is utilized to Yang–Mills fields in general.
The textual content includes a wealth of precise and rigorous computations and may attract mathematicians and physicists, in addition to complex undergraduate and graduate scholars, attracted to functions of differential geometry to actual theories equivalent to basic relativity, effortless particle physics and quantum gravity.