Modern Differential Geometry in Gauge Theories

This 2-volume research monograph presents a new kind of modern differential geometry approach to such physical theories as gauge theory. Sheaf theory (geometry) and sheaf cohomology (analysis) are used to explain all the machinary of classical differential geometry without any notion of smoothness. Together they present Maxwell fields, YangMills fields and general relativity. These texts contains a treasure trove of minutely detailed and rigorous computations. This original work will appeal to advanced undergraduates, graduate students, mathematicians and physicists interested in applications of differential geometry to physical theories.

Original, well-written work of interest Presents for the first time (physical) field theories written in sheaf-theoretic language Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments Author's mastery of the subject and the rigorous treatment of this text make it invaluable

Contenu
Maxwell Fields: General Theory.- The Rudiments of Abstract Differential Geometry.- Elementary Particles: Sheaf-Theoretic Classification, by Spin-Structure, According to Selesnick's Correspondence Principle.- Electromagnetism.- Cohomological Classification of Maxwell and Hermitian Maxwell Fields.- Geometric Prequantization.