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Elements for Physics

Quantities, Qualities, and Intrinsic Theories

  • Albert┬áTarantola

Table of contents

  1. Front Matter
    Pages I-XXII
  2. Pages 11-77
  3. Back Matter
    Pages 153-263

About this book

Introduction

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 if 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.

Keywords

Invariance Lie groups Manifolds Theoretical physics mathematical physics physics quality

Authors and affiliations

  • Albert┬áTarantola
    • 1
  1. 1.Institut de Physique du Globe de ParisParis Cedex 05France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-31107-2
  • Copyright Information Springer Berlin Heidelberg 2006
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-540-25302-0
  • Online ISBN 978-3-540-31107-2
  • Buy this book on publisher's site
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