Geometric Algebra for Physicists and over one million other books are available for Amazon Kindle. Learn more

Vous voulez voir cette page en français ? Cliquez ici.


or
Sign in to turn on 1-Click ordering.
or
Amazon Prime Free Trial required. Sign up when you check out. Learn More
More Buying Choices
Have one to sell? Sell yours here
Start reading Geometric Algebra for Physicists on your Kindle in under a minute.

Don't have a Kindle? Get your Kindle here, or download a FREE Kindle Reading App.

Geometric Algebra for Physicists [Paperback]

Chris Doran , Anthony Lasenby
5.0 out of 5 stars  See all reviews (3 customer reviews)
List Price: CDN$ 103.95
Price: CDN$ 83.16 & FREE Shipping. Details
You Save: CDN$ 20.79 (20%)
o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o
Only 1 left in stock (more on the way).
Ships from and sold by Amazon.ca. Gift-wrap available.
Want it delivered Monday, April 21? Choose One-Day Shipping at checkout.

Formats

Amazon Price New from Used from
Kindle Edition CDN $50.53  
Hardcover --  
Paperback CDN $83.16  

Book Description

Dec 10 2007 0521715954 978-0521715959 1
This book is a complete guide to the current state of geometric algebra with early chapters providing a self-contained introduction. Topics range from new techniques for handling rotations in arbitrary dimensions, the links between rotations, bivectors, the structure of the Lie groups, non-Euclidean geometry, quantum entanglement, and gauge theories. Applications such as black holes and cosmic strings are also explored.

Customers Who Bought This Item Also Bought


Product Details


Product Description

Review

Review of the hardback: 'I would therefore highly recommend this book for anyone wishing to enter this interesting and potentially fundamental area.' Mathematics Today

'The range of topics presented in the book is astonishing. ... The present book is intended for physicists, but mathematicians will also find it highly valuable. The exposition of Grassmann's algebra given at the beginning of the book is exceptionally clear and is written with a light touch. ... It is extraordinarily well written and is a beautifully produced piece.' The Mathematical Gazette

Book Description

Geometric Algebra has advanced rapidly in the last ten years, becoming an important topic in the physics and engineering communities. As leading experts in the field the authors have led many of these new developments. This book provides an introduction to the subject covering applications such as black hole physics and quantum computing. Suitable as a textbook for graduate courses on the physical applications of geometric algebra, this book is also a valuable reference for all researchers working in the fields of relativity and quantum theory.

Inside This Book (Learn More)
Browse and search another edition of this book.
First Sentence
The goal of expressing geometrical relationships through algebraic equations has dominated much of the development of mathematics. Read the first page
Explore More
Concordance
Browse Sample Pages
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
Search inside this book:

Customer Reviews

4 star
0
3 star
0
2 star
0
1 star
0
5.0 out of 5 stars
5.0 out of 5 stars
Most helpful customer reviews
5.0 out of 5 stars Physics done right June 16 2010
Format:Paperback
The more familiar we are with a particular technique, the harder it is to see its limitations. For those who have taken the appropriate courses, the machinery of real and complex numbers, vectors, matrices, and so on, seem to be the inevitable "right" way of doing things. Yet there is another way, pioneered in the nineteenth century by Grassmann (1844) and Clifford (1878) and called (by Clifford) "geometric algebra" (GA). For over a century, GA was buried by the "standard" approach of Hamilton, Gibbs, et al., but it has recently been resurrected by a small but dedicated group of people, perhaps most notably by David Hestenes in "New Foundations for Classical Mechanics" (1999).

"Geometric Algebra for Physicists" performs the monumental task of presenting almost all of basic physics, from the Lorentz transformation to the Schwarzchild metric, with an excursion into quantum theory on the way, in the notation of GA. Since most physicists seem to be fairly happy with the notations that they grew up with, it is fair to ask "Why bother?". The authors' answer is "In [GA] much of the standard subject matter taught to physicists can be formulated in an elegant and highly condensed fashion". Here's just one example: on page 230, Maxwell's equations are given in the form "del F = J" (in which del is a GA operator, not the standard operator used to define div, grad, etc.).

This is not a book for bedtime reading: you will need at least an undergraduate degree in mathematics or physics to get much out of it, and even then you will have to master an unfamiliar, but very powerful, notation. With that background, you could skim through and say "Wow!" or you could spend a few years studying the development in detail; either way, the book is worth every penny. You might also want to consider "Geometric Algebra for Computer Science" by Dorst et al.
Was this review helpful to you?
5.0 out of 5 stars Compared to what ? Jan. 29 2004
By A Customer
Format:Hardcover
This is truly a great book for any one who is interested in not just physics, but physical reality. Although the ideas expressed therein have a long history and are by no means as uniquely those of its authors as were Albert Einstein's in his day, I believe that they will have comparable lasting value. Moreover the synthesis presented in this book, which builds pre-eminently on the work of Hestenes, is absolutely superb. Interested readers need not take my word for these claims, but are invited to prove it to themselves.
Although the above should be a sufficient review, my experience nevertheless indicates that it is a good idea to warn potentially enthusiastic readers against several common semantic misconceptions, lest they jump to conclusions which prevent them from ever taking that vital first step. Thus let it be clearly understood that Geometric Algebra is NOT:
(1) A replacement for linear/matrix/tensor algebra (on the contrary, it is a very nice complement to these formalisms).
(2) Identical, or even very close, to Emil Artin's earlier excellent book on bilinear forms with the title "Geometric Algebra".
(3) Another name for the enormous field "algebraic geometry" (it is indeed appropriate that the word stemming from "geometry" comes first in "geometric algebra").
(4) Just another reformulation of complex / quaternion / octonian analysis; for it connects all these purely algebraic objects, and many generalizations thereof, to Felix Klein's Erlangen Programme and Sophus Lie's theory of continuous groups.
(5) The ultimate theory of everything (although it probably will eventually be found to have something to do with it).
Read more ›
Was this review helpful to you?
5.0 out of 5 stars Articulate Path to the Future July 18 2003
Format:Hardcover
The quality and importance of this book could hardly be overstated. Geometric algebra might casually be considered the "correct" generalization of linear algebra. By considering, for a start, directed line segments, the linear algebra courses presently taught in some high schools and all universities achieve miracles. Although viewed by a few of the slower students as merely unpleasant bookkeeping systems, linear algebra derives its power from allowing algebraic manipulation of sophisticated aggregate objects, namely vectors. The benefits are not just computational, but stem more importantly from a more powerful and more unified, although slightly more abstract point of view than a student had before studying. Geometric algebra is all that and much more. By extending consideration from directed line segments to the inclusion of direct plane segments, directed elements of three space, etc., an extremely flexible and elegant mathematical tool arises. It allows a deeper, quicker, and more concise treatment of essentially all of modern differential geometry. Its applications throughout physics are at once simplifications of ordinary matrix treatments and occasions to allow much greater insight.
Geometric algebra is a great theory, one of highest importance. It will, undoubtedly, find a dominant place in our mathematics curriculum at the highest speed allowed by our educational systems (the highest speed being actually quite slow). This book is an especially good place to begin study. It starts from the most elementary principles, and exposes the material with very thoughtful, clear presentation.
Read more ›
Was this review helpful to you?
Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com: 4.7 out of 5 stars  7 reviews
96 of 101 people found the following review helpful
5.0 out of 5 stars Compared to what ? Jan. 29 2004
By A Customer - Published on Amazon.com
Format:Hardcover
This is truly a great book for any one who is interested in not just physics, but physical reality. Although the ideas expressed therein have a long history and are by no means as uniquely those of its authors as were Albert Einstein's in his day, I believe that they will have comparable lasting value. Moreover the synthesis presented in this book, which builds pre-eminently on the work of Hestenes, is absolutely superb. Interested readers need not take my word for these claims, but are invited to prove it to themselves.
Although the above should be a sufficient review, my experience nevertheless indicates that it is a good idea to warn potentially enthusiastic readers against several common semantic misconceptions, lest they jump to conclusions which prevent them from ever taking that vital first step. Thus let it be clearly understood that Geometric Algebra is NOT:
(1) A replacement for linear/matrix/tensor algebra (on the contrary, it is a very nice complement to these formalisms).
(2) Identical, or even very close, to Emil Artin's earlier excellent book on bilinear forms with the title "Geometric Algebra".
(3) Another name for the enormous field "algebraic geometry" (it is indeed appropriate that the word stemming from "geometry" comes first in "geometric algebra").
(4) Just another reformulation of complex / quaternion / octonian analysis; for it connects all these purely algebraic objects, and many generalizations thereof, to Felix Klein's Erlangen Programme and Sophus Lie's theory of continuous groups.
(5) The ultimate theory of everything (although it probably will eventually be found to have something to do with it).
Geometric algebra IS a practical and natural (canonical) tool for formulating physical and mathematical problems in homogeneous spaces in a fully covariant fashion. But more importantly, you do not need to understand all those words in order to benefit from it, and this book is an excellent place for physicists of all stripes to start.
75 of 78 people found the following review helpful
5.0 out of 5 stars A powerful mathematical language for physics and engineering July 31 2004
By Prof C. R. PAIVA - Published on Amazon.com
Format:Hardcover
This is a well-written book on a very interesting and important subject: geometric algebra (GA) is a powerful and elegant mathematical language -- based on the works of Hamilton, Grassmann and Clifford -- that is especially well-suited for spacetime physics and several fields of engineering.

The authors adopt David Hestenes' viewpoint of a graded GA as a unified mathematical language that is coordinate-free, thereby stressing the fundamental role of geometric invariants in physics.

In fact, the elementary vector analysis -- which pervades almost all undergraduate (and even) graduate approaches to electrodynamics -- finds its roots in the misguided Gibbsian approach: Gibbs advocated abandoning Hamilton's quaternions and just work with scalar and cross products of vectors. However, the cross product has a major flaw: it only exists in three (or seven) dimensions -- if we require that (i) it should have just two factors, (ii) to be orthogonal to the factors, and (iii) to have length equal to the corresponding parallelogram.

Electrodynamics and relativistic physics, particularly, are elegantly presented through GA and otherwise cumbersome calculations may be circumvented in a simple and insightful way.

Mainstream physics and engineering cannot overlook GA anymore.
33 of 33 people found the following review helpful
5.0 out of 5 stars makes your head buzz... Aug. 4 2007
By rewt - Published on Amazon.com
Format:Hardcover
I'm reading this book somewhat in parallel with Hestenes' New Foundations for Classical Mechanics. Both are fantastic books (Hestenes' predates this one), and in some parts they are complementary, while of course they overlap in the foundations and many special topics. What is so fascinating about Geometric Algebra and Calculus? I think it's mainly the recognition that many seemingly complicated theorems of mathematical physics really become much clearer - in a sense of getting a guts feeling about the geometry. The method opens a way to look at the same thing from totally different angles: If one can't imagine something based on geometric arguments, one can take the presented formalism and translate it back into geometry, and suddenly things become clear.
Is the book (or that by Hestenes) basic and easy to understand or are they difficult? Certainly they require some work by the reader. To follow the entire book, one really can't do without learning to master the formalism of geometric algebra, which is simple, yet sometimes bizarre. I suspect though that it is only bizarre to the one who "knows it all" already: The student or scientist who has grown familiar with vector spaces, matrix notation and wiggling around with tensor notation, needs to go through the same exercises as the bloody beginner to whom even the idea of a vector may not be clear. In fact, the beginner could be at a real advantage to not being poisoned by vector calculus. For example, take the very basic notation for a geometric product of two multi-vectors: ab = a.b + a^b (the sum of inner and outer product). What's so confusing about it? Nothing, really, after one really understands what "+" here means. But it happens often enough that one only thinks about this product in terms of the right hand side of the equation, because those are totally familiar for anyone who took basic linear algebra, and then ends up making simple things complicated again. I must say that it was like loosing shadows from the eyes to see how the formulations in this book and Hestenes' work explain so well why it is that the quantum mechanical psi function needs to be complex, or better yet what really the i means in physics, and how the entire set of Maxwell equations (all 4 of them) are one simple continuity equation. That's the kind of thing that makes your head buzz. I'm not done with these books, but I have a clear feeling that in the end I will have an entry point to understand QM and parts of general relativity not just formally (especially QM) but really develop a guts feeling for it.
One thing that I'm still a bit missing in any of the books related to geometric algebra is classical continuum mechanics. This may be so because many of the authors are immersed in fields related to cosmology. In this book, one can find a tiny little bit also about elasticity (linear and nonlinear). However, I keep wondering what it would be like to reformulate the entire underlying theory of continuum mechanics (about deforming solids, elastic or viscoelastic or plastic, about fluid flow, about polarized materials, biological active materials, etc). Could something new be learned? I bet it could!
20 of 20 people found the following review helpful
4.0 out of 5 stars definitely for physicists May 16 2009
By Peeter Joot - Published on Amazon.com
Format:Paperback
This book has a good introduction to geometric algebra. This includes an excellent axiomatic presentation, unlike the Hestenes New Foundations book where the basic identities are presented rather randomly.

The title of this book "for Physicists", is very accurate. This book assumes a great deal of physics knowledge and many subjects are not covered in enough detail for comprehensibility for first time study. With an engineering education, much of the physics in this book is over my head. Many important details are treated very much more briefly than I would personally like. This is justifiable unfortunately since the book would otherwise be three thousand pages long.

In order to understand the parts of this book that I have now covered, I have had to also go off on the side and learn aspects of relativity, tensors, electromagnetism, Lagrangians, Noether's theorem, and much more (QM and more relativity and more E&M are next on my list before returning to this book).

Studying this text continues to be a fun project, and if I ever finish this book I believe I will have a fairly good understanding of basic physics. Despite being a very hard book to grasp due to brevity and advanced topics, taking the time to work through the details provides valuable insights, and yields approaches that would not be obvious with only traditional formulations.
59 of 82 people found the following review helpful
5.0 out of 5 stars Articulate Path to the Future July 18 2003
By Jim Curry - Published on Amazon.com
Format:Hardcover
The quality and importance of this book could hardly be overstated. Geometric algebra might casually be considered the "correct" generalization of linear algebra. By considering, for a start, directed line segments, the linear algebra courses presently taught in some high schools and all universities achieve miracles. Although viewed by a few of the slower students as merely unpleasant bookkeeping systems, linear algebra derives its power from allowing algebraic manipulation of sophisticated aggregate objects, namely vectors. The benefits are not just computational, but stem more importantly from a more powerful and more unified, although slightly more abstract point of view than a student had before studying. Geometric algebra is all that and much more. By extending consideration from directed line segments to the inclusion of direct plane segments, directed elements of three space, etc., an extremely flexible and elegant mathematical tool arises. It allows a deeper, quicker, and more concise treatment of essentially all of modern differential geometry. Its applications throughout physics are at once simplifications of ordinary matrix treatments and occasions to allow much greater insight.
Geometric algebra is a great theory, one of highest importance. It will, undoubtedly, find a dominant place in our mathematics curriculum at the highest speed allowed by our educational systems (the highest speed being actually quite slow). This book is an especially good place to begin study. It starts from the most elementary principles, and exposes the material with very thoughtful, clear presentation. The economy and elegance of the geometric algebra itself allows this one substantial but not enormous book to reveal great insights into many branches of study, from differential geometry and its applications to gravity theory to quantum mechanics and classical mechanics.
If I had no books in my library, I would purchase a Bible. If I had only the Bible in my library, I would purchase this book next. I would certainly study this book in all detail before making a third purchase. My library already has several books in it. None of them will be read further until I finish every line, every exercise of this book. It's an important theory, and it is explained in a very useful and articulate way. This would, of course, be entirely expected if the authors were from Oxford University. Since they are only from Cambridge, we might not have expected as much, but we got it, nonetheless.
Search Customer Reviews
Only search this product's reviews
ARRAY(0xb209c438)

Look for similar items by category


Feedback