Geometry of the Fundamental Interactions On Riemann's Legacy to High
Gravitation, electromagnetics and the two types of nuclear forces constitute the four fundamental forces of nature which regulate our everyday life. Amazingly, they are all described by a single idea of the 19th century proposed by Bernhard Riemann,
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M.D. Maia
Geometry of the Fundamental Interactions On Riemann’s Legacy to High Energy Physics and Cosmology
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M.D. Maia Universidade de Brasilia Institute of Physics 70910-000 Brasilia D.F. Brazil [email protected]
ISBN 978-1-4419-8272-8 e-ISBN 978-1-4419-8273-5 DOI 10.1007/978-1-4419-8273-5 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011925657 c Springer Science+Business Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Artwork by Diego Moscardini Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
The four fundamental forces in nature, gravitation, electromagnetic, weak, and strong nuclear forces, are based on a single idea of the 19th century, the Riemann curvature. The vast amount of experimental data and theoretical development in high energy physics has confirmed that concept. Only very recently, Einstein’s gravitational field, which originated the geometric paradigm for physics, has shown signs that it needs an improvement to explain the gravitational observations in modern cosmology, where Einstein’s gravitational field can describe only about 4% of the gravitational interaction in the universe. On the other hand, at the quantum scale Einstein’s gravitational field has resisted all attempts to quantization. Therefore, something appears to be missing to complete the idea of Riemann. In the past 20 years we have debated with colleagues, teachers, collaborators, and students on the different forms in which geometry and the physics of the fundamental interactions mix. The overall feeling is that the understanding of the geometry of the fundamental interactions has become too complex to grasp within the standard professional lifetime of a graduate student of physics, mathematics, astronomy, and engineering to understand what is going on, specially within the current productivity syndrome. Hence the proposal of this book to supply a blend of what is known and what is not explained. Therefore, the program of this book is about theoretical research with emphasis on inducing a debate, whenever possible, on how to fix and improve existing theories which have reached their applicability and prediction limits. We start with concepts of physical space since Kant, going through the evolution of the idea of space– time, symmetries and its ass
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