Modern Differential Geometry in Gauge Theories ( Yang-Mills Fields, Vol. 2) - Softcover

Mallios, Anastasios

Softcover

ISBN 10: 0817643796 ISBN 13: 9780817643799

Publisher: Birkhäuser, 2009

Synopsis

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

About this title

From the Back Cover:

Differential geometry, in the classical sense, is developed through the theory of smooth manifolds. Modern differential geometry from the author’s perspective is used in this work to describe physical theories of a geometric character without using any notion of calculus (smoothness). Instead, an axiomatic treatment of differential geometry is presented via sheaf theory (geometry) and sheaf cohomology (analysis). Using vector sheaves, in place of bundles, based on arbitrary topological spaces, this unique approach in general furthers new perspectives and calculations that generate unexpected potential applications.

Modern Differential Geometry in Gauge Theories is a two-volume research monograph that systematically applies a sheaf-theoretic approach to such physical theories as gauge theory. Beginning with Volume 1, the focus is on Maxwell fields. All the basic concepts of this mathematical approach are formulated and used thereafter to describe elementary particles, electromagnetism, and geometric prequantization. Maxwell fields are fully examined and classified in the language of sheaf theory and sheaf cohomology. Continuing in Volume 2, this sheaf-theoretic approach is applied to Yang–Mills fields in general.

The text contains a wealth of detailed and rigorous computations and will appeal to mathematicians and physicists, along with advanced undergraduate and graduate students, interested in applications of differential geometry to physical theories such as general relativity, elementary particle physics and quantum gravity.

Review:

From the reviews:

“This book is the sequel to [Modern differential geometry in gauge theories. Vol. I: Maxwell fields. Boston, MA: Birkhäuser (2006; Zbl 1116.18006)], continuing the study of gauge theories in the framework of abstract differential geometry. It consists of four chapters. ... All in all, the book is well written, and it is recommendable to novices and specialists.” (Hirokazu Nishimura, Zentralblatt MATH, Vol. 1185, 2010)

About this edition

• Publisher: Birkhäuser
• Publication date: 2009
• ISBN 10: 0817643796
• ISBN 13: 9780817643799
• Binding: Paperback
• Edition number: 1
• Number of pages: 253