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Reviews and extends the theory of Lie groups, develops differential geometry, and adapts the usual notion of linear tangent application
Includes supplementary material: sn.pub/extras
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Table of contents (4 chapters)
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Front Matter
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Back Matter
About this book
While usual presentations of physical theories emphasize the notion of physical quantity, this book shows that there is much to gain when introducing the notion of physical quality. The usual physical quantities simply appear as coordinates over the manifolds representing the physical qualities. This allows to develop physical theories that have a degree of invariance much deeper than the usual one. It is shown that properly developed physical theories contain logarithms and exponentials of tensors: their conspicuous absence in usual theories suggests, in fact, that the fundamental invariance principle stated in this book is lacking in present-day mathematical physics. The book reviews and extends the theory of Lie groups, develops differential geometry, proposing compact definitions of torsion and of curvature, and adapts the usual notion of linear tangent application to the intrinsic point of view proposed for physics. As an illustration, two simple theories are studied with some detail, the theory of heat conduction and the theory of linear elastic media. The equations found differ quantitatively and qualitatively from those usually presented.
Authors and Affiliations
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Institut de Physique du Globe de Paris, Paris Cedex 05, France
Albert Tarantola
About the author
Professor at the University of Paris. Doctor Honoris Causa by the University of Copenhagen. Silver medal of the French National Science Foundation. Author of a well-known book on Inverse Problem Theory.
Bibliographic Information
Book Title: Elements for Physics
Book Subtitle: Quantities, Qualities, and Intrinsic Theories
Authors: Albert Tarantola
DOI: https://doi.org/10.1007/978-3-540-31107-2
Publisher: Springer Berlin, Heidelberg
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2006
Hardcover ISBN: 978-3-540-25302-0Published: 01 December 2005
Softcover ISBN: 978-3-642-06452-4Published: 12 February 2010
eBook ISBN: 978-3-540-31107-2Published: 30 December 2006
Edition Number: 1
Number of Pages: XIV, 266
Number of Illustrations: 34 b/w illustrations, 10 illustrations in colour
Topics: Mathematical Methods in Physics, Engineering, general