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Modern Differential Geometry in Gauge Theories

Yang–Mills Fields, Volume II

Authors: Mallios, Anastasios

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  • An original, well-written work of broad interest
  • First presentation of field theories written in sheaf-theoretic language
  • Offers numerous minutely detailed, rigorous computations
  • The author's mastery of the subject makes this book invaluable
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eBook $69.99
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  • ISBN 978-0-8176-4634-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
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  • Immediate eBook download after purchase
Softcover $89.99
price for USA in USD
  • ISBN 978-0-8176-4379-9
  • Free shipping for individuals worldwide
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About this book

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.

Reviews

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)

Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook $69.99
price for USA in USD (gross)
  • ISBN 978-0-8176-4634-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA in USD
  • ISBN 978-0-8176-4379-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Modern Differential Geometry in Gauge Theories
Book Subtitle
Yang–Mills Fields, Volume II
Authors
Copyright
2010
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-4634-9
DOI
10.1007/978-0-8176-4634-9
Softcover ISBN
978-0-8176-4379-9
Edition Number
1
Number of Pages
XIX, 234
Number of Illustrations
5 b/w illustrations
Topics