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These 1, Sur La Structure Des Groupes De Transformations Finis Et Continus; These 2, Propositions Donnees Par La Faculte. This Book Is In French. ... Read more

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This book describes the life and achievements of the great French mathematician, Elie Cartan. Here readers will find detailed descriptions of Cartan's discoveries in Lie groups and algebras, associative algebras, differential equations, and differential geometry, as well of later developments stemming from his ideas. There is also a biographical sketch of Cartan's life. A monumental tribute to a towering figure in the history of mathematics, this book will appeal to mathematicians and historians alike. ... Read more

Product Description
Describes orthgonal and related Lie groups, using real or complex parameters and indefinite metrics. Develops theory of spinors by giving a purely geometric definition of these mathematical entities. Covers generalities on the group of rotations in n-dimensional space, the theory of spinors in spaces of any number of dimensions and much more.
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Customer Reviews (5)

translated from French
We have Weyl, Pauli, Dirac and Cartan to thank for our modern
theory of groups in physics. This book published in 1937
has none of the later Lie algebra representations of the Cartan generalization of groups
and thus, like Weyl's similar book may deceive the reader into thinking
he understands when he has only a rough and not very even
introduction to these groups. This book doesn't reach much higher than SU(2),
SO(3) and the Dirac U(1)*SU(2)*SU(2).
The standard model of physics deals with the symmetry breaking of SU(5)
( the Cartan A_4 group) to U(1)*SU(2)*SU(3). The Lie algebras and
irreducible Cartan representations of such higher symmetries
will demand the student read further than this text.
So this book is an historical introduction that gives the starting basis
for the mathematics needed by modern students in physics and chemistry.

The most important book that I have ever read
This is also the most difficult book that I have read, it is poorly written. Everybody that I have recommended it to has given up on it. There is scarcely a page in this book that when properly understood is not a key to understanding something in physics. The second chapter on multivectors is worth more than every book that I have read on vectors. Unless things have changed since I taught physics, most people who use vectors have a shallow knowledge of them. One example is the bivector, which we have been taught are axial vectors that are somehow different from regular vectors, polar vectors. Actually they define planes and the so-called axial vector is perpendicular to the plane. In standard physics, nothing happens along the axial vector, e.g. rotation or magnetic field, because the action takes place on the plane of the bivector. It is also interesting that each of the four Maxwell equations is a different type of multivector. And it seems to me that the search for a magnetic charge is futile because the Maxwell equation would require it to be a trivector, known to most people as a triple scalar product. This would require a single number to change sign when you go from a right to left-handed coordinate system.

This book is a case of very hard work paying off. What is really needed is a rewrite of this book in more comprehensible form.

Masterpiece based on the original lecture notes of Cartan
This book is a great work on the subject of spinors. Since it is based solely on Elie Cartan's work, the termonology and wording reflects that of the transition coming out of the Post-Victorian math era (i.e., when quaternions and the more abstract mathematics where used for applied calculations in physics, which have been replaced with scalars and vectors). The geometrical definition layed down in the third chapter makes this a very comprehensive book for the newcomer to the subject. Quote page 42., "A spinor is thus a sort of "directed" or "polarized" isotropic vector; a rotation about an axis through an angle of 2pi changes the polarization of this isotropic vector."

Review of theory of spinors
This is an excellent introductory book on spinors, the basic mathematical object used to represent particles with spin.

The author begins by defining the spinor as a form of a square root of a 3 dimensional nullvector.Scalars, vectors and tensors are then described by theirproperties under simple geometrical transformations such as reflection androtation.The author then represents vectors as 2x2 matrices.Thetransformational properties of spinors are defined by their relation tovectors and tensors under these same simple transformations.The authorthen shows how spinors are useful for finding the irreduciblerepresentations of the rotation group.These concepts are then extended tohigher dimensional spinors.Specific applications are shown for Laplace'sequation, the Dirac equation and to general relativity.

The is anintroductory, inexpensive, brief and easy to read book.The book alsocovers a fair amount of ground.It is an excellent first book for thesubject.It does not contain modern developments in the field or someelements of the current notational system for representing spinors.Yet,for me it was the first book that gave me a sense of really understandingthe significance of the Dirac equation and quantum physic's concept ofspin.

Review of theory of spinors
This is an excellent introductory book on spinors, the basic mathematical object used to represent particles with spin.

The author begins by defining the spinor as a form of a square root of a 3 dimensional nullvector.Scalars, vectors and tensors are then described by theirproperties under simple geometrical transformations such as reflection androtation.The author then represents vectors as 2x2 matrices.Thetransformational properties of spinors are defined by their relation tovectors and tensors under these same simple transformations.The authorthen shows how spinors are useful for finding the irreduciblerepresentations of the rotation group.These concepts are then extended tohigher dimensional spinors.Specific applications are shown for Laplace'sequation, the Dirac equation and to general relativity.

The is anintroductory, inexpensive, brief and easy to read book.The book alsocovers a fair amount of ground.It is an excellent first book for thesubject.It does not contain modern developments in the field or someelements of the current notational system for representing spinors.Yet,for me it was the first book that gave me a sense of really understandingthe significance of the Dirac equation and quantum physic's concept ofspin. ... Read more

Customer Reviews (1)

very hard to get what they are talking about
The problem discussed mainly seems to be:
Rij=0
which if Rij refers to the Ricci curvature tensor
is or is very like the null Ricci problem that resulted inmodern Calibi-Yau
theory. They seems to respect each other, but not their
different approaches to the mathematics involved.
I got this book trying find something on their
joint theory of spin based general relativity,
but this book is about what parallel means in terms of tensors
and functions inside a spherical manifold, I think.
More interesting than the context is the subtext
of two of the most important men of the 20th century
exchanging nearly polite letters like this
and having them collected and published. ... Read more

Product Description
Elie Cartan's book "Geometry of Riemannian Manifolds" (1928) was one of the best introductions to his methods. It was based on lectures given by the author at the Sorbonne in the academic year 1925-26. A modernized and extensively augmented edition appeared in 1946 (2nd printing, 1951; 3rd printing, 1988). Cartan's lectures in 1926-27 were different - he introduced exterior forms at the very beginning and used orthogonal frames throughout to investigate the geometry of Riemannian manifolds. In this course, he solved a series of problems in Euclidean and non-Euclidean spaces, as well as a series of variational problems on geodesics. The lectures were translated into Russian in the book "Riemannian Geometry in an Orthogonal Frame" (1960). This book has many innovations, such as the notion of intrinsic normal differentiation and the Gaussian torsion of a submanifold in a Euclidean multidimensional space or in a space of constant curvature, an affine connection defined in a normal fibre bundle of a submanifold, and so on. This book was available neither in English nor in French. It has now been translated into English by Vladislav V.Goldberg, currently Distinguished Professor of Mathematics at the New Jersey Institute of Technology, USA, who edited the Russian edition. ... Read more

Customer Reviews (1)

once overview, twice not suitable yet
As with all great masterpieces of math, I am not a critic for a good critique assumes expertise. I am an expert self-study beginner in pure and applied mathematics. My comments is for people in that disposition.
If you get a first look at the inside, then you quickly learn that the notation is very hard to understand for an introductory textbook. In addition, it is very dense and concise. Not much of an explanation to help first time beginners. It isn't meant to be introductory! I am sure that it is a standard classic for experts.
Elie Cartan was a truly great differential geometer! That is the reason I have the book; it's from a master.
In terms of approachability of the book, it is not that aproachable. If you are studying differential geometry, then it maybe right for you. I can say that I wanted an introductory self-study book and was disappointed.
It remains on the bookself and even got lost among other books for later review. When I have some more differential geometry courses or time I will try to decipher the notation. I can read math at the undergraduate level. This book is for sure for graduate students!
I just hope that in the future I can still make use of the book. I plan to go study differential geometry as a course with a professor. Then it would be nice to have something like this for reference work.
All in all, a masterpiece not easy to understand. It is how works of genius is. I better stick to reading math history books for introductions to math and self-studies. A better elementary book on Vector and Tensor Analysis is by Harry Lass which covers the fundamentals for elementary beginners like me. If you like Harry Lass's book then look forward to my other reviews. I am a struggling beginner that is not yet in graduate school for pure mathematics. Preparation is key and this book is an indication of what is ahead.
... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles!Élie Joseph Cartan (9 April 1869 - 6 May 1951) was an influential French mathematician, who did fundamental work in the theory of Lie groups and their geometric applications. He also made significant contributions to mathematical physics, differential geometry, and group theory. He was the father of another influential mathematician, Henri Cartan. Élie Cartan was born in the village of Dolomieu in Isère a department of France, the son of a blacksmith. He became a student at the École Normale Supérieure in Paris in 1888 and obtained his doctorate in 1894. He subsequently held lecturing positions in Montpellier and Lyon, becoming a professor in Nancy in 1903. He took a lecturing position at the Sorbonne in Paris in 1909, becoming professor there in 1912 until his retirement in 1940. He died in Paris after a long illness. ... Read more

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pp. 107-120 ... Read more

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In the mathematical field of differential geometry, a Cartan connection is a flexible generalization of the notion of an affine connection. It may also be regarded as a specialization of the general concept of a principal connection, in which the geometry of the principal bundle is tied to the geometry of the base manifold using a solder form. Cartan connections describe the geometry of manifolds modelled on homogeneous spaces. The theory of Cartan connections was developed by Élie Cartan, as part of (and a way of formulating) his method of moving frames (repère mobile). It operates with differential forms and so is computational in character. The main idea is to develop a suitable notion of the connection forms and curvature using moving frames adapted to the particular geometrical problem at hand. For instance, in relativity or Riemannian geometry, orthonormal frames are used to obtain a description of the Levi-Civita connection as a Cartan connection. For Lie groups, Maurer?Cartan frames are used to view the Maurer?Cartan form of the group as a Cartan connection. ... Read more

Customer Reviews (1)

Does Not Add Up to Value
Very poor value for money here.BIG price for Wikipedia downloads.If Kama exists, the three "editors" will be edited out of the earth's biosphere. Pleae do not fund evil.

Wikipedia is on the net for free. ... Read more

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High Quality Content by WIKIPEDIA articles! In mathematics, and specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms. Historically, connection forms were introduced by Élie Cartan in the first half of the 20th century as part of, and one of the principal motivations for, his method of moving frames. The connection form generally depends on a choice of frame, and so is not a tensorial object. Various generalizations and reinterpretations of the connection form were formulated subsequent to Cartan's initial work. In particular, on a principal bundle, a principal connection is a natural reinterpretation of the connection form as a tensorial object. On the other hand, the connection form has the advantage that it is a differential form defined on the differentiable manifold, rather than on an abstract principal bundle over it. Hence, despite their lack of tensoriality, connection forms continue to be used because of the relative ease of performing calculations with them. In physics, connection forms are also used broadly in the context of gauge theory, through the gauge covariant derivative. ... Read more

Customer Reviews (1)

Does not add up to value
Very poor value for money here.BIG price for Wikipedia downloads.

Wikipedia is on the net for free. ... Read more

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High Quality Content by WIKIPEDIA articles! Théophile Ernest de Donder (1872 ? 1957) was a Belgian mathematician and physicist famous for his 1923 work in developing correlations between the Newtonian concept of chemical affinity and the Gibbsian concept of free energy. He was professor between 1911 and 1942, at the Université Libre de Bruxelles. Initially he continued the work of Henri Poincaré and Elie Cartan. As from 1914 he was influenced by the work of Albert Einstein and was an enthusiastic proponent of the theory of relativity. He gained significant reputation in 1923, when he developed his definition of chemical affinity. He pointed out a connection between the chemical affinity and the Gibbs free energy. ... Read more

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This digital document is an article from Science and Its Times, brought to you by Gale®, a part of Cengage Learning, a world leader in e-research and educational publishing for libraries, schools and businesses.The length of the article is 593 words.The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase.You can view it with any web browser.The histories of science, technology, and mathematics merge with the study of humanities and social science in this interdisciplinary reference work. Essays on people, theories, discoveries, and concepts are combined with overviews, bibliographies of primary documents, and chronological elements to offer students a fascinating way to understand the impact of science on the course of human history and how science affects everyday life. Entries represent people and developments throughout the world, from about 2000 B.C. through the end of the twentieth century. ... Read more