Book Description
This text is a self-contained, comprehensive treatment of the tensor and spinor calculus of space-time manifolds with as few technicalities as correct treatment allows. Both the physical and geometrical motivation of all concepts are discussed, helping the reader to go through the technical details in a confident manner. Several physical theories are discussed and developed beyond standard treatment using results in the book. Both the traditional "index" and modern "coordinate-free" notations are used side-by-side in the book, making it accessible to beginner graduate students in mathematics and physics. The methods developed offer new insights into standard areas of physics, such as classical mechanics or electromagnetism, and takes readers to the frontiers of knowledge of spinor calculus.
Customer Reviews:
superbly written.......2002-11-23
I highly recommend this book to anyone interested in spinor calculus. The authors' primary goal is to investigate the problem of defining Lie and covariant differentiation of spinor fields. This they do, but in addition, they carefully cover a number of standard topics and a number that I'd not seen elsewhere (such as the decomposition of a connection into constituents including the contorsion & metric-incompatibility tensors) in an extremely lucid way.
Book Description
This volume introduces and systematically develops the calculus of 2-spinors. This is the first detailed exposition of this technique which leads not only to a deeper understanding of the structure of space-time, but also provides shortcuts to some very tedious calculations. Many results are given here for the first time.
Customer Reviews:
Complete introduction to spinors and space-time physics.......2006-04-16
This book provides a very comprehensive account of two-spinor calculus, along with some of its applications to physics. This material is intrinsically interesting and has some applications to physics, in addition it also provides the background needed to study volume II. The second volume covers applications to physics in more detail and twistors too.
Spinors unquestionably play a central role in quantum mechanics. Some problems in general relativity are certainly more transparent when approached with spinors, as compared to the usual tensor analysis. This combined with the fact that one can roughly view a spinor as the square root of a null vector and considering things like Dirac's scissors suggest the possibility that spinors are more fundamental than tensors and may provide a deeper insight into the nature of space-time than tensors do. This is one of the main themes of the book, I personally find the arguments intriguing.
The first two chapters establish the geometry and algebra of spinors. The pace is reasonable and the approach is very geometrical. Then the correspondence between tensors and spinors is developed. First the authors show how to represent tensors as spinors and then they show how to represent spinors as tensors. As an application of this they show how a Lorentz transformation is represented by two spin transformations. This is followed by a chapter that takes many concepts from differential geometry and puts them in spinor form, including Einstein's equation.
The final chapter mostly considers fields formulated in terms of spinors. This includes the electromagnetic field, Yang-Mills fields (a nice introduction to fibre bundles is included) and general relativity.
On the whole I think this book provides an excellent development of two-spinor calculus, with a nice emphasis on the geometry of spinors. It takes some familiar fields, such as the electromagnetic field, and formulates them in terms of spinors. However, one thing I thought was missing was more extended discussions of the known situations in general relativity where spinor methods prove more useful than tensor methods, e.g. the classification of the Weyl tensor or Witten's proof of the positive energy theorem. More material like this is presented in volume II. This book also gives some general arguments that spinors may be more fundamental than tensors and hence provide more insight into the nature of space-time, in fact this is one of the central themes of the book. I find the arguments to be very plausible, but I think it's safe to say that even twenty years after the publication of the book that it has yet to be demonstrated.
Book Description
Spinor and Twistor Methods in Space-Time Geometry introduces the theory of twistors, and studies in detail how the theory of twistors and 2-spinors can be applied to the study of space-time. Twistors have, in recent years, attracted increasing attention as a mathematical tool and as a means of gaining new insights into the structure of physical laws. This volume also includes a comprehensive treatment of the conformal approach to space-time infinity with results on general-relativistic mass and angular momentum, a detailed spinorial classification of the full space-time curvature tensor, and an account of the geometry of null geodesics.
Customer Reviews:
Twistors from their creator.......2006-04-16
The first volume of this set provided a through development of two-spinor calculus. This book, the second volume, uses two-spinor calculus to analyze some problems in physics. It examines situations where spinor methods unquestionably provide value, such as Witten's proof of the positive energy theorem. It also introduces twistors (only briefly mentioned in volume I). The original goal of twistor theory was very ambitious, to essentially quantize space-time by making it a concept derived from twistor space. Obviously that hasn't be achieved, but that goal isn't a primary focus of this book.
The first chapter is a quick recap of volume I, including most of the formulas from it that are used in this book. After this, twistors are introduced. The algebra is easy to follow, but there is a lot of it. A geometric description of null twistors is given in terms of the spinors it's composed of. Later it's shown how to construct a null twistor, up to a phase factor, from the momentum and spin of a massless particle. I thought this provided a nice physical model. One of the interesting things is that conformal invariance has a fairly central role, as it does in string theory. Overall the contact with physics in this chapter is fairly light.
From this point on application to physics are more central, of course there is still plenty of math. The first topic considered is congruences of null geodesics. A couple of things stand out. One is the coverage is more complete than usual. The other is that the authors describe the relation of twistors to shear free ray congrucences, normally it's only spinors that are used to describe the congruences.
The next chapter covers on of the more widely used applications of spinor methods to general relativity, the classification of the Weyl tensor. While this is perhaps the most widely discussed application of spinors in general relativity, the depth of the discussion here is much greater than the usual. Instead of just showing how much more transparent the analysis is with spinors, this book also adds a twist that cannot be done with tensors, it considers changing the phase and magnitude of the Weyl spinor, i.e. it considers more than the principal null directions. There is also material on the classification of the Ricci curvature, which is uncommon.
Following this spinors are applied to asymptotic questions in general relativity. The chapter begins with a review of causal structure and compactification (compactification in the sense of conformal compactification, not in the sense of wrapping extra dimensions in a small torus). The view that space-time points are entities derived from twistor space is further developed here, but still not in great detail. For me the best parts of this, rather long, chapter were the discussions of peeling properties of gravitational radiation the use of spinors and twistors to analyze energy-momentum and angular momentum. Regarding the latter, it also includes the use of spinors to prove the positive energy theorem.
I liked this book a lot, even more than volume I. One thing that surprised me is that I expected more development of twistor theory, there was a fair amount, but I would have liked to have seen more. A lot of the material in this book is clearly relevant to physics, however there is also a substantial amount that is more speculative.
Average customer rating:
|
Introduction to 2-Spinors in General Relativity
Peter O'Donnell
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover
 Astrophysics & Space Science
| Astronomy
| Science
| Subjects
| Books
General
| Science
| Subjects
| Books
General
| Applied
| Mathematics
| Science
| Subjects
| Books
General
| Mathematics
| Science
| Subjects
| Books
General
| Physics
| Science
| Subjects
| Books
Mathematical Physics
| Physics
| Science
| Subjects
| Books
Relativity
| Physics
| Science
| Subjects
| Books
General
| Nuclear Physics
| Physics
| Science
| Subjects
| Books
Astrophysics & Space Science
| Astronomy
| Professional Science
| Professional & Technical
| Subjects
| Books
General
| Physics
| Professional Science
| Professional & Technical
| Subjects
| Books
Mathematical Physics
| Physics
| Professional Science
| Professional & Technical
| Subjects
| Books
Nuclear Physics
| Physics
| Professional Science
| Professional & Technical
| Subjects
| Books
Relativity
| Physics
| Professional Science
| Professional & Technical
| Subjects
| Books
All Titles
| Qualifying Textbooks - Fall 2007
| Stores
| Books
Similar Items:
-
Spinors and Space-Time (Cambridge Monographs on Mathematical Physics)
-
The Theory of Spinors
-
The Road to Reality: A Complete Guide to the Laws of the Universe
ASIN: 9812383077 |
Book Description
This book deals with 2-spinors in general relativity, beginning by developing spinors in a geometrical way rather than using representation theory, which can be a little abstract. This gives the reader greater physical intuition into the way in which spinors behave. The book concentrates on the algebra and calculus of spinors connected with curved space-time. Many of the well-known tensor fields in general relativity are shown to have spinor counterparts. An analysis of the Lanczos spinor concludes the book, and some of the techniques so far encountered are applied to this. Exercises play an important role throughout and are given at the end of each chapter.
Average customer rating:
|
Advances in Analysis and Geometry: New Developments Using Clifford Algebras (Trends in Mathematics)
Manufacturer: Birkhäuser Basel
ProductGroup: Book
Binding: Hardcover
General
| Science
| Subjects
| Books
General
| Algebra
| Pure Mathematics
| Mathematics
| Science
| Subjects
| Books
Linear
| Algebra
| Pure Mathematics
| Mathematics
| Science
| Subjects
| Books
Number Theory
| Pure Mathematics
| Mathematics
| Science
| Subjects
| Books
General
| Mathematics
| Science
| Subjects
| Books
Mathematical Analysis
| Mathematics
| Science
| Subjects
| Books
Probability & Statistics
| Applied
| Mathematics
| Science
| Subjects
| Books
Statistics
| Applied
| Mathematics
| Professional Science
| Professional & Technical
| Subjects
| Books
Mathematical Analysis
| Mathematics
| Professional Science
| Professional & Technical
| Subjects
| Books
General
| Algebra
| Pure Mathematics
| Mathematics
| Professional Science
| Professional & Technical
| Subjects
| Books
Linear
| Algebra
| Pure Mathematics
| Mathematics
| Professional Science
| Professional & Technical
| Subjects
| Books
Number Theory
| Pure Mathematics
| Mathematics
| Professional Science
| Professional & Technical
| Subjects
| Books
All Amazon Upgrade
| Amazon Upgrade
| Stores
| Books
Professional & Technical
| Amazon Upgrade
| Stores
| Books
Science
| Amazon Upgrade
| Stores
| Books
All Titles
| Qualifying Textbooks - Fall 2007
| Stores
| Books
Professional
| Qualifying Textbooks - Fall 2007
| Stores
| Books
Science
| Qualifying Textbooks - Fall 2007
| Stores
| Books
ASIN: 3764366613 |
Book Description
The study of systems of special partial differential operators that arise naturally from the use of Clifford algebra as a calculus tool lies in the heart of Clifford analysis. The focus is on the study of Dirac operators and related ones, together with applications in mathematics, physics and engineering. At the present time, the study of Clifford algebra and Clifford analysis has grown into a major research field. There are two sources of papers in this collection. One is from a satellite conference to the ICM 2002 in Beijing, held August 15-18 at the University of Macau; and the other stems from invited contributions by top-notch experts in the field.
Average customer rating:
- Nobel prize winning material.
|
General Relativity and Matter: A Spinor Field Theory from Fermis to Light-Years (Fundamental Theories of Physics)
M. Sachs
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover
General
| Science
| Subjects
| Books
General
| Physics
| Science
| Subjects
| Books
Mathematical Physics
| Physics
| Science
| Subjects
| Books
Relativity
| Physics
| Science
| Subjects
| Books
General
| Physics
| Professional Science
| Professional & Technical
| Subjects
| Books
Mathematical Physics
| Physics
| Professional Science
| Professional & Technical
| Subjects
| Books
All Titles
| Qualifying Textbooks - Fall 2007
| Stores
| Books
Professional
| Qualifying Textbooks - Fall 2007
| Stores
| Books
Science
| Qualifying Textbooks - Fall 2007
| Stores
| Books
ASIN: 9027713812 |
Customer Reviews:
Nobel prize winning material........1997-06-20
This book represents a world change in Physics as fundamental as the works of Newton and Einstein. The theory is a remarkable extension of the work of Einstein in his later years. Professor Sachs is a master of clear and lucid writing. A true masterpiece !
Gravity and Electromagnetism are now naturally married in a brilliant re-derivation of Einstein's General Theory of Relativity. Sachs uncovers a long forgotten paper by Einstein and Mayer that holds the secret. But Einstein missed its fundamental importance. The vector basis used by Einstein in deriving the General Theory is incomplete. Just as Maxwell (and Tait) used the more complete basis of quaternions in deriving Maxwell's equations, Sachs builds a complete theory of General Relativity but using a quaternionic basis. Hamilton and his quaternions are finally vindicated.
The "square root problem" of the fundamental metric defining space-time disappears with the natural factorization of the metric stated in a quaternionic basis. The true nature of spin that has eluded all the vendors of Quantum Mechanics comes simply from the correct application of relativistic covariance. It does NOT depend on the quantum mechanical nature of the description per se.
The additional key insight is that Sachs realises that Einstein needed to eliminate the discrete symmetries of reflections in space and time. Sachs points out that the theory of relativity compares laws of nature in reference frames that are distinguished from each other ONLY in terms of their relative motion - a continuous set of transformations.
Sachs can lay a strong claim to having merged all the known forces in this brilliant work. It is a fairly reasonable hypothesis that the ONLY forces in nature are NOW shown to be Gravity and Electromagnetism. The Strong and Weak forces are simply aspects of Gravity and Electromagnetism at an extremely short range. Sachs demonstrates in a mathematical tour de force that all of nature appears to be contained in his equations from nuclear dimensions all the way through to the properties of astronomical objects. An oscillating Universe cosmology naturally arises instead of the Big Bang discontinuity. All discontinuities fade away into the smooth continuous fabric of Sach's space-time continuum.
I suspect there will be many years before the true nature of this staggering leap of Sachs is recognized. Meanwhile Physics wanders in the wilderness of the string theory and other well meaning but misguided theories that come from academics wandering too far from the shirt-tails of geniuses like Einstein and Newton.
Average customer rating:
- Solid and very useful, but be careful
- Good introduction to spinors & related group theory
- Have Your Pen Ready
- An Excellent Introduction To Groups and Advanced Q.M.
|
Spinors in Physics (Graduate Texts in Contemporary Physics)
Jean Hladik
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover
General
| Science
| Subjects
| Books
General
| Applied
| Mathematics
| Science
| Subjects
| Books
General
| Mathematics
| Science
| Subjects
| Books
General
| Physics
| Science
| Subjects
| Books
Mathematical Physics
| Physics
| Science
| Subjects
| Books
Quantum Theory
| Physics
| Science
| Subjects
| Books
General
| Nuclear Physics
| Physics
| Science
| Subjects
| Books
General
| Physics
| Professional Science
| Professional & Technical
| Subjects
| Books
Mathematical Physics
| Physics
| Professional Science
| Professional & Technical
| Subjects
| Books
Quantum Theory
| Physics
| Professional Science
| Professional & Technical
| Subjects
| Books
General
| Physics
| Sciences
| New & Used Textbooks
| Stores
| Books
Quantum Mechanics
| Physics
| Sciences
| New & Used Textbooks
| Stores
| Books
All Amazon Upgrade
| Amazon Upgrade
| Stores
| Books
Professional & Technical
| Amazon Upgrade
| Stores
| Books
Science
| Amazon Upgrade
| Stores
| Books
All Titles
| Qualifying Textbooks - Fall 2007
| Stores
| Books
Professional
| Qualifying Textbooks - Fall 2007
| Stores
| Books
Science
| Qualifying Textbooks - Fall 2007
| Stores
| Books
ASIN: 0387986472 |
Book Description
Invented by Dirac in creating his relativistic quantum theory of the electron, spinors are important in quantum theory, relativity, nuclear physics, atomic and molecular physics, and condensed matter physics. Essentially, they are the mathematical entities that correspond to electrons in the same way that ordinary wave functions correspond to classical particles (including photons). Because of their relations to the rotation group SO(n) and the unitary group SU(n), the discussion should be of interest to applied mathematicians as well as physicists.
Customer Reviews:
Solid and very useful, but be careful.......2006-01-12
Yes, it's true: this book does have a ton of typos in it, so it might be best to find an online errata listing or something when you purchase it.
However, the book, despite a bit of a wobbly start, will definitely teach you most everything you need to know about spinors. The best things about it are that it ties the material to physics very strongly and often, and it has solutions immediately following the exercises! Also, everything is explained in a very precise and explicit manner.
Good introduction to spinors & related group theory.......2001-05-19
I've browsed through a number of books looking for a good, approachable, understandable, etc. introduction to spinors and their use in physics. This book is it. It does have an unfortunately large number of misprints/typos, but if you actually READ the material, make an attempt to understand it, and work out the examples and derivations of equations in the text, then you know where the mistakes are. I have an errata sheet a mile long that I intend to send to the publisher!
The book also covers, in a very understandable way, some introductory material on Lie groups and Lie algebras.
I would have given 5 stars but for the large number of typos. Still, I would highly recommend this book for anyone interested in the use of spinors in physics.
The contents are:
I Spinors in Three-Dimensional Space 1. Two-Component Spinor Geometry 2. Spinors and SU(2) Group Representations 3. Spinor Representation of SO(3) 4. Pauli Spinors
II Spinors in Four-Dimensional Space 5. The Lorentz Group 6. Representations of the Lorentz Group 7. Dirac Spinors 8. Clifford and Lie Algebras
Appendix: Groups and Their Representations
Have Your Pen Ready.......2001-05-08
Simply horrible. This book is littered with mistakes. I had bought this hoping to have a more or less complete reference to spinor theory. Instead I now have a book that is more confusing than helpful. If you do not have a good, even if basic, background in spinors do not buy this. Luckily I did and could see this was a poorly done book. I would suggest using Lounesto instead.
An Excellent Introduction To Groups and Advanced Q.M........2000-01-16
This book is divided into two parts. The first part introduces spinors in 3D and the second in space-time. It is very readable and includes detailed solutions to many problems with an appendix including essential group theory. I strongly recommend this book to be used along with relativistic quantum mechanics and quantum fields.
Book Description
This systematic and self-contained treatment of the theory of three-dimensional spinors and their applications fills an important gap in the literature. Without using the customary Clifford algebras frequently studied in connection with the representations of orthogonal groups, spinors are developed in this work for three-dimensional spaces in a language analogous to the spinor formalism used in relativistic spacetime.
Unique features of this work:
* Systematic, coherent exposition throughout
* Introductory treatment of spinors, requiring no previous knowledge of spinors or advanced knowledge of Lie groups
* Three chapters devoted to the definition, properties and applications of spin-weighted functions, with all background given.
* Detailed treatment of spin-weighted spherical harmonics, properties and many applications, with examples from electrodynamics, quantum mechanics, and relativity
* Wide range of topics, including the algebraic classification of spinors, conformal rescalings, connections with torsion and Cartan's structural equations in spinor form, spin weight, spin-weighted operators and the geometrical meaning of the Ricci rotation coefficients
* Bibliography and index
This work will serve graduate students and researchers in mathematics and mathematical and theoretical physics; it is suitable as a course or seminar text, as a reference text, and may also be used for self-study.
Books:
- Geotechnical Engineering: Principles and Practices
- Green to Gold: How Smart Companies Use Environmental Strategy to Innovate, Create Value, and Build Competitive Advantage
- Group Theory and Quantum Mechanics
- Handbook of Heat Transfer
- Handbook of Heat Transfer
- High-Power Diode Lasers: Fundamentals, Technology, Applications (Topics in Applied Physics)
- History: Fiction or Science? (Chronology, No. 1)
- History: Fiction or Science? (Chronology, No. 1)
- History: Fiction or Science? (Chronology, No. 1)
- History: Fiction or Science? (Chronology, No. 1)
Books Index
Books Home
Recommended Books
- Food and Beverage Cost Control
- Eat That Frog!: 21 Great Ways to Stop Procrastinating and Get More Done in Less Time
- All About Techniques in Pastel
- Baltic States Insight Guide
- Designing and Developing Multimedia: A Practical Guide for the Producer, Director, and Writer
- Ethan Frome
- Cotswold Gardens
- Real Life Notes: Reflections and Strategies for Life After Graduation
- Business Process Reengineering: Breakpoint Strategies for Market Dominance
- Big M, little m Marketing: New Strategies for a New Asia
General Relativity (Springer Undergraduate Mathematics Series)
Statistical Mechanics (Vol. 4 of Pauli Lectures on Physics) (Pauli Lectures on Physics)
Quantum Field Theory
Supersymmetry and String Theory: Beyond the Standard Model
