This is to let you know that Springer has accepted that my new book,
Elements for Physics, is freely available for download (http://
www.ipgp.jussieu.fr/~tarantola/Files/Professional/Books) (it can also
be purchased at Amazon.com :-)
Best regards,
Albert Tarantola
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Elements for Physics : Quantities, Qualities, and Intrinsic Theories
by Albert Tarantola, Springer, 2006
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.