The Theory of Spinors (Dover Books on Mathematics) by Élie Cartan (PDF)

Description

The French mathematician Élie Cartan (1869–1951) was one of the founders of the modern theory of Lie groups, a subject of central importance in mathematics and also one with many applications. In this volume, he describes the orthogonal groups, either with real or complex parameters including reflections, and also the related groups with indefinite metrics. He develops the theory of spinors (he discovered the general mathematical form of spinors in 1913) systematically by giving a purely geometrical definition of these mathematical entities; this geometrical origin makes it very easy to introduce spinors into Riemannian geometry, and particularly to apply the idea of parallel transport to these geometrical entities.The book is divided into two parts. The first is devoted to generalities on the group of rotations in n-dimensional space and on the linear representations of groups, and to the theory of spinors in three-dimensional space. Finally, the linear representations of the group of rotations in that space (of particular importance to quantum mechanics) are also examined. The second part is devoted to the theory of spinors in spaces of any number of dimensions, and particularly in the space of special relativity (Minkowski space). While the basic orientation of the book as a whole is mathematical, physicists will be especially interested in the final chapters treating the applications of spinors in the rotation and Lorentz groups. In this connection, Cartan shows how to derive the “Dirac” equation for any group, and extends the equation to general relativity.One of the greatest mathematicians of the 20th century, Cartan made notable contributions in mathematical physics, differential geometry, and group theory. Although a profound theorist, he was able to explain difficult concepts with clarity and simplicity. In this detailed, explicit treatise, mathematicians specializing in quantum mechanics will find his lucid approach a great value.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Muy bueno.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.

⭐Clear, and a joy to read. But if you are a student of modern physics, I suggest a more modern treatment in context. For those wanting to know the “why’s and wherefore’s” of spinors, Cartan’s book will be exactly what you want. I really should have given it 5 stars, but I reserve five for only the greatest classics. Note, this is an out-of-date text. But sometimes these grand old texts can fill in some questions, especially concerning motivation, better than more modern treatments. If you’d like an introduction to where it all came from, this is the book for you!

⭐Although written in the early 20th century, this short text on spinors actually contains a great background for some of the fundamental concepts needed to understand Quantum Mechanics (the Dirac equation in particular) and Loop Quantum Gravity.And, unlike most textbooks, it’s less than $10 (paperback).So, a very economical way to get a great start in learning some really interesting math.Also, the translation is well written and surprisingly easy to follow, especially for a guy like me (engineer, not mathematician.)

⭐I bought the paperback version more than 10 years ago, and I left it at my hometown. This year I wanted to read it and I bought the Kindle version. The content is fine of course, but not the format — the letters along with any superscrits/subscripts in most equations are way too small and cannot be enlarged even when one has enlarge the paragraph texts. I found this happen in the Kindle versions of other physics books, too. Using Android device (cell phones, pads, …) bring such results; one can only use the Cloud Reader on the browsers over a Windows PC or laptop to read in a far more comfortable way, at least this is true for the time being (2015 August). As for iOS users, I don’t know. I am simply not an Apple fan. Hope the technicians can fix this problem soon…

⭐The style, presentation, format and so on are old and cumbersome to read in the eyes of a modern educated individual. I found other books on the topic of Spinors but written at a higher level of understanding were easier due to the aging of this book. Wouldn’t particularly suggest this title to anybody not interested in seeing the work of the originator of spinors.

⭐E. Cartan is a master in mathematics. This book is one of his famous monographs. In this book, the moving frame method is introduced to describe the spin. It is suitable for not only the mathematicians but also the physicists.

⭐This book does not work on a Kindle Paper-white. The font of most of the critical equations is invisible and can not be enlarged. It does however work on Kindle for the PC. The content is excellent but it fails on portability.

⭐Cartan is not just one of the greats but a masterly writer and teacher. Not least compared to the obfuscation and vanity etc. that pervade so many newer texts presenting the same topics. Not least it helps the reader to make sense of the newer works because the detail he presents helps earth understanding without their pervasive loading up of more advanced topics like category and cohomology theories.

⭐ok

Keywords

Free Download The Theory of Spinors (Dover Books on Mathematics) in PDF format
The Theory of Spinors (Dover Books on Mathematics) PDF Free Download
Download The Theory of Spinors (Dover Books on Mathematics) 2012 PDF Free
The Theory of Spinors (Dover Books on Mathematics) 2012 PDF Free Download
Download The Theory of Spinors (Dover Books on Mathematics) PDF
Free Download Ebook The Theory of Spinors (Dover Books on Mathematics)