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. Uses a unifying illustration: two simple theories are studied with some detail, the theory of heat conduction and the theory of linear elastic media. Shows that the resulting equations derived in this manner differ quantitatively and qualitatively from those usually presented.
Elements for Physics
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From the Back Cover
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.
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.
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Inside This Book
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First Sentence:
Even when the physical space (or space-time) is assumed to be flat, some of the "tensors" appearing in physics are not elements of a linear space, but of a space that may have curvature and torsion. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
oriented geodesic segment, linear mapping that maps, ideal elastic medium, linear space tangent, logarithmic image, linear tangent space, troupe operation, incompressibility modulus, characteristic tensor, geometric sum, group manifold, tangent mapping, connection manifold, stiffness tensor, ordinary sum, elastic energy density, geodesic segments, finite neighborhood, parallel transport, metric coordinate, compliance tensor, stress space, affine parameter, torsion tensor, metric manifold Key Phrases - Capitalized Phrases (CAPs): (learn more)
Intrinsic Physical Theories, Tangent Autoparallel Mappings, Ideal Elasticity, Geotensors Definition New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Even when the physical space (or space-time) is assumed to be flat, some of the "tensors" appearing in physics are not elements of a linear space, but of a space that may have curvature and torsion. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
oriented geodesic segment, linear mapping that maps, ideal elastic medium, linear space tangent, logarithmic image, linear tangent space, troupe operation, incompressibility modulus, characteristic tensor, geometric sum, group manifold, tangent mapping, connection manifold, stiffness tensor, ordinary sum, elastic energy density, geodesic segments, finite neighborhood, parallel transport, metric coordinate, compliance tensor, stress space, affine parameter, torsion tensor, metric manifold Key Phrases - Capitalized Phrases (CAPs): (learn more)
Intrinsic Physical Theories, Tangent Autoparallel Mappings, Ideal Elasticity, Geotensors Definition New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 7
books:
See all 7 books this book cites
- Maximum Entropy and Bayesian Methods (Fundamental Theories of Physics) by Kenneth M. Hanson in Back Matter
- Matrix Theory, Vol. 2 by Felix R. Gantmacher in Back Matter
- Handbook of Chemistry and Physics, 68th Edition by Robert C. Weast in Back Matter
- Acta Numerica 2002: Volume 11 by Arieh Iserles in Back Matter
- Lectures on Lie Groups and Lie Algebras (London Mathematical Society Student Texts) by Roger W. Carter in Back Matter
See all 7 books this book cites
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