Overview
Explains some of the most complex theories in physics in clear and understandable language
Provides comprehensive information about three of the four fundamental forces of nature
Offers an explanation of Yang-Mills theory, with many theoretical properties given in the form of examples
Includes supplementary material: sn.pub/extras
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Table of contents (11 chapters)
Keywords
About this book
The Yang-Mills theory of gauge interactions is a prime example of interdisciplinary mathematics and advanced physics. Its historical development is a fascinating window into the ongoing struggle of mankind to understand nature. The discovery of gauge fields and their properties is the most formidable landmark of modern physics. The expression of the gauge field strength as the curvature associated to a given connection, places quantum field theory in the same geometrical footing as the gravitational field of general relativity which is naturally written in geometrical terms. The understanding of such geometrical property may help one day to write a unified field theory starting from symmetry principles.
Of course, there are remarkable differences between the standard gauge fields and the gravitational field, which must be understood by mathematicians and physicists before attempting such unification. In particular, it is important to understand why gravitation is not a standard gauge field.
This book presents an account of the geometrical properties of gauge field theory, while trying to keep the equilibrium between mathematics and physics. At the end we will introduce a similar approach to the gravitational field.
Reviews
From the reviews:
“The book, with a good amount of rigor, takes a ‘slice’ of all the aspects of the unifying math, and aligns them with Riemann geometry, and especially the Riemann tensor. … Highly recommended for those who want a fresh view of the real, current applications and value of Riemann, all the way beyond quaternions to octavians!” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, December, 2013)Authors and Affiliations
Bibliographic Information
Book Title: Geometry of the Fundamental Interactions
Book Subtitle: On Riemann's Legacy to High Energy Physics and Cosmology
Authors: M. D. Maia
DOI: https://doi.org/10.1007/978-1-4419-8273-5
Publisher: Springer New York, NY
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer Science+Business Media, LLC 2011
Hardcover ISBN: 978-1-4419-8272-8Published: 27 June 2011
Softcover ISBN: 978-1-4899-9024-2Published: 01 October 2014
eBook ISBN: 978-1-4419-8273-5Published: 14 June 2011
Edition Number: 1
Number of Pages: IX, 179
Topics: Theoretical, Mathematical and Computational Physics, Geometry, Elementary Particles, Quantum Field Theory, Field Theory and Polynomials