Twistor Geometry and Field Theory (Cambridge Monographs on Mathematical Physics)

Book Description

This book deals with the twistor treatment of certain linear and non-linear partial differential equations in mathematical physics. The description in terms of twistors involves algebraic and differential geometry, and several complex variables, and results in a different kind of setting that gives a new perspective on the properties of space-time and field theories. The book is designed to be used by mathematicians and physicists and so the authors have made it reasonably self-contained. The first part contains a development of the necessary mathematical background. In the second part, Yang-Mills fields and gravitational fields (the basic fields of contemporary physics) are described at the classical level. In the final part, the mathematics and physics are married to solve a number of field-theoretical problems.

Customer Reviews:

not so easy ..........2007-08-07

I'm another one of the "total idiots" physicists. Unfortunately, I wasn't so lucky with the book. While I find here and there a few pages that I can understand without too much stress, there are other parts that caused me to abort reading - symbol stack overflow. Why do I get the impression that others here may rate this as a five star book simply to express their (probably well deserved) pride to have understood some of it? It's more than just a little difficult to read this book. They call this an introduction?

beautifully written.......2004-07-29

From the mathematical point of view, this is an enjoyable read; it could even serve as a first exposure to algebraic topology.

It is without question that Penrose's remarkable insights have come a long way in helping physicists foster new mathematical ideas, and put them on solid footing; and this is what the authors have set out to do. It is written in a very clear and lucid style, and it is the most comprehensive expository work in mathematical physics that I have seen in a long time.
-A

A model of clarity.......2004-01-09

This is an extremely well written book. Couldn't be more clear. The authors derserve an AMS award for clarity of exposition. They even explain to physicists (read mathematical idiots) what a sheaf cohomolgy is. Hats raised to their efforts.

An Introduction to Twistor Theory (London Mathematical Society Student Texts)

Average customer rating:

Good introduction

An Introduction to Twistor Theory (London Mathematical Society Student Texts)
S. A. Huggett , and K. P. Tod
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

General | Physics | Science | Subjects | Books

Waves & Wave Mechanics | Physics | Science | Subjects | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books
Similar Items:

Spinors and Space-Time (Cambridge Monographs on Mathematical Physics)
Spinors and Space-Time (Cambridge Monographs on Mathematical Physics)
Twistor Geometry and Field Theory (Cambridge Monographs on Mathematical Physics)
The Theory of Spinors
The Road to Reality: A Complete Guide to the Laws of the Universe

ASIN: 0521451574

Book Description

This book is an introduction to twistor theory and modern geometrical approaches to space-time structure at the graduate or advanced undergraduate level. It will be valuable also to the physicist as an introduction to some of the mathematics that has proved useful in these areas, and to the mathematician as an example of where sheaf cohomology and complex manifold theory can be used in physics.

Customer Reviews:

Good introduction.......2006-04-10

I think this book gives a very good introduction to twistor theory. However, it's not an elementary book. Readers should already be familiar with topology, differential geometry, group theory and general relativity. The book is short, as are the chapters, and it gets to the point quickly. I consider it primarily a math book, but aspects of physics are frequently considered.

After a quick introduction and review of tensors the concept of spinors is introduced. It's the usual approach drawing a correspondence between a vector and a rank (1,1) spinor. In particular between a null vector and the product of a spinor with its own conjugate. This is often informally phrased by saying a spinor is the square root of a vector.

Following this the spinor algebra is developed. At this point it is shown how to formulate tensor algebra in terms of spinors (with some bits of projective geometry thrown in). Although the book is developing the mathematics of spinors some familiarity with physics is required to appreciate all the discussion. Without some background in physics, relativity in particular, the significance of this might be missed. Applications considered include: Einstein's equation, the Weyl tensor, principle null directions and the classification of spacetime, Dirac neutrinos, source free Maxwell equations and congruences of null vectors. I would have like to have seen more discussion about the advantages of the spinor formulation, for example, how it makes classifying algebraically special spacetimes simpler.

Twistors are introduced next, this is about one-third of the way through the book. Although the correspondence between twistor space and null geodesics is considered; the original motivation of twistors, to provide a theory of quantum spacetime, isn't emphasized.

The rest of the book mainly contains chapters explaining various applications of twistor theory. They mostly have very physics sounding names like "The non-linear graviton" or "The twisted photon and Yang-Mills construction". My favorite chapter was the one covering Penrose's quasi-local momentum and quasi-local angular momentum. I may have missed something, but with the exception of this chapter I'm not sure any of the others offered any new insights to the world of physics.

On the whole I thought this was a very good book. I liked the pace and the text was clear. It even includes hints to some of the exercises. However, it does require a bit of background knowledge, I would especially recommend being familiar with topology. Obviously it's not as comprehensive as Penrose and Rindler or Ward and Wells, but it's very good for building a foundation.

Superstrings and the Search for the Theory of Everything

Average customer rating:

Just what I was looking for
Excellent Introduction!
For neither the scientist or the layman
Exposes frontier issues & jargon in particle physics
Should be called Roger Penrose attempt to expose his work

Superstrings and the Search for the Theory of Everything
F. David Peat
Manufacturer: McGraw-Hill
ProductGroup: Book
Binding: Paperback

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

General | Physics | Science | Subjects | Books

Quantum Theory | Physics | Science | Subjects | Books

Superstrings: A Theory of Everything? (Canto)
Synchronicity: The Bridge Between Matter and Mind
The Search for Superstrings, Symmetry, and the Theory of Everything
In Search of Schrödinger's Cat: Quantum Physics and Reality
The Trouble With Physics: The Rise of String Theory, The Fall of a Science, and What Comes Next

ASIN: 0809242575

Book Description

"Peat grapples with these amazingly recondite notions and succeeds brilliantly in making them clear." --Publishers Weekly

Customer Reviews:

Just what I was looking for.......2007-08-03

Reading an overview about modern thoughts on unifying the physics of particles, relativity and the forces of nature has been on my to do list for a while. Mission accomplished, albeit based on 1988 physics. If there was a more recent follow-up book by F. David Peat I would buy it; there is a lot of content that only wet my appetite to learn more about the details behind the narrative and I have enjoyed the way the author wove this complicated story together.

Excellent Introduction!.......2004-01-22

I found this book to be an excellent introduction to some fascinating fields in theoretical physics. It is easy to read and was hard for me to put down. I am not a Mathematician or a Physicist but this book has done a lot to pique my interest and motivate me to tackle the Math required for a deeper inquiry into these fascinating subjects. I look forward to reading more books by this author.

For neither the scientist or the layman.......2000-06-16

As a scientist familiar with quantum theory, but not a physicist, this book was very frustrating to read. I felt satisfied neither as a layman or a physical chemist. The book quoted several key concepts of superstring theory but did not really explain them in a way that I felt gave me more than a very superficial overview of the field. The digression into twistors was made at a point where more space could have fruitfully been spent adding flesh to the concepts presented early in the book.

Exposes frontier issues & jargon in particle physics.......1999-08-03

This book is non-technical -- it has almost no equations, but is well-illustrated. Just having finished it, I feel it gave a good sense of the major issues involved in this still highly speculative and uncertain field. Readable summary of the state-of-the-art in 1988. Author condescends nicely to the reader: he takes pains to repeat over and over, in slightly varying words, the technical points; this made book wordy; but it was a good strategy since, w/o equations, these esoteric ideas come across vaguely at best. Repetition allows at least "ear knowledge" of the jargon. Please don't expect much more at this level.

Like another reviewer, I was not happy with one-third of the book being devoted to twistors, since these strike this outsider as higher on mathematical elegance than on physical content. I will not fault Peat, however, for doing this since: A) due to his friendship with the Penrose Twistor group he is specially qualified to popularise this subject, and B) the Twistor program, a child of Penrose's brain, is rich in guiding principles, and provides therefore a healthy antidote to the superstrings, which grew up higgeldy-piggeldy by a sequence of "accidental" discoveries -- "It seems to work, but, heck, we don't really know why." Twistors have been less a matter of trial and error. At least they work well for massless particles. (Sidelight: In a blackboard discussion w/ Penrose at Cal Tech that I chanced to overhear about 25 yrs. ago, Feynman told Penrose that no one had succeeded in making massless fields cohere together so as to act like massive fields.)

Should be called Roger Penrose attempt to expose his work.......1999-02-18

The book starts of good and in chapter 7 he breaks of completely from superstrings and starts talking about some new unheard of idea of things called twisters. This would not be bad but twisters are supposed to replace spiners. Spiners to the uninformed are just a very small part of superstring theory.An example is writing a book on a 1998 Corvette and writing about the car for 6 chapers, then the other chapters are about the plug wires. Very Disapointing. If you want to read about some real superstring theory buy any book by Michio Kaku, much, much better books. They actually stick to what they say their about.

Applications of Analytic and Geometric Methods to Nonlinear Differential Equations (NATO Science Series C:)

Average customer rating:

Applications of Analytic and Geometric Methods to Nonlinear Differential Equations (NATO Science Series C:)

Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

Mathematical Analysis | Mathematics | Science | Subjects | Books

Mathematical Physics | Physics | Science | Subjects | Books

All Amazon Upgrade | Amazon Upgrade | Stores | Books

Professional & Technical | Amazon Upgrade | Stores | Books

Science | Amazon Upgrade | Stores | Books
ASIN: 0792324579

Book Description

In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years. (1) The inverse scattering transform (IST), using complex function theory, which has been employed to solve many physically significant equations, the `soliton' equations. (2) Twistor theory, using differential geometry, which has been used to solve the self-dual Yang--Mills (SDYM) equations, a four-dimensional system having important applications in mathematical physics. Both soliton and the SDYM equations have rich algebraic structures which have been extensively studied.
Recently, it has been conjectured that, in some sense, all soliton equations arise as special cases of the SDYM equations; subsequently many have been discovered as either exact or asymptotic reductions of the SDYM equations. Consequently what seems to be emerging is that a natural, physically significant system such as the SDYM equations provides the basis for a unifying framework underlying this class of integrable systems, i.e. `soliton' systems. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods.
The majority of nonlinear evolution equations are nonintegrable, and so asymptotic, numerical perturbation and reduction techniques are often used to study such equations. This book also contains articles on perturbed soliton equations. Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations.

(ABSTRACT)
In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years; the inverse scattering transform (IST), for `soliton' equations and twistor theory, for the self-dual Yang--Mills (SDYM) equations. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. Additionally, it contains articles on perturbed soliton equations, Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations.

Fundamental Interactions and Twistor-like Methods: XIX Max Born Symposium (AIP Conference Proceedings / Mathematical and Statistical Phsyics)

Average customer rating:

Fundamental Interactions and Twistor-like Methods: XIX Max Born Symposium (AIP Conference Proceedings / Mathematical and Statistical Phsyics)

Manufacturer: American Institute of Physics
ProductGroup: Book
Binding: Hardcover

General | Earth Sciences | Science | Subjects | Books

General | Science | Subjects | Books

General | Physics | Science | Subjects | Books

Mathematical Physics | Physics | Science | 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: 0735402523

Book Description

All papers were peer reviewed. The volume contains reports on work done in areas of field theory, supersymmetry, string theory, higher spins, and related topics using group-theoretical and geometrical methods which involve, one way or another, twistor-like techniques (singletons, harmonics, superembeddings, and twistors themselves).

Further Advances in Twistor Theory, Volume III: Curved Twistor Spaces

Average customer rating:

Further Advances in Twistor Theory, Volume III: Curved Twistor Spaces

Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Paperback

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

General | Physics | Science | Subjects | Books

General | Medicine | Subjects | Books

General | Computers & Internet | Subjects | Books
ASIN: 1584880473

Book Description

Although twistor theory originated as an approach to the unification of quantum theory and general relativity, twistor correspondences and their generalizations have provided powerful mathematical tools for studying problems in differential geometry, nonlinear equations, and representation theory. At the same time, the theory continues to offer promising new insights into the nature of quantum theory and gravitation. Further Advances in Twistor Theory, Volume III: Curved Twistor Spaces is actually the fourth in a series of books compiling articles from Twistor Newsletter-a somewhat informal journal published periodically by the Oxford research group of Roger Penrose. Motivated both by questions in differential geometry and by the quest to find a twistor correspondence for general Ricci-flat space times, this volume explores deformed twistor spaces and their applications. Articles from the world's leading researchers in this field-including Roger Penrose-have been written in an informal, easy-to-read style and arranged in four chapters, each supplemented by a detailed introduction. Collectively, they trace the development of the twistor programme over the last 20 years and provide an overview of its recent advances and current status.

Further Advances in Twistor Theory: The Penrose Transform and Its Applications (Research Notes in Mathematics Series)

Average customer rating:

Further Advances in Twistor Theory: The Penrose Transform and Its Applications (Research Notes in Mathematics Series)
L. J. Mason , and L. P. Hughston
Manufacturer: Longman Sc & Tech
ProductGroup: Book
Binding: Paperback

General | Science | Subjects | Books

General | Physics | Science | Subjects | Books

Waves & Wave Mechanics | Physics | Science | Subjects | Books

Integrability, Self-Duality, and Twistor Theory (London Mathematical Society Monographs New Series)

Average customer rating:

Integrability, Self-Duality, and Twistor Theory (London Mathematical Society Monographs New Series)
L. Mason , and N. M. J. Woodhouse
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

General | Physics | Science | Subjects | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books
ASIN: 0198534981

Book Description

It has been known for some time that many of the familiar integrable systems of equations are symmetry reductions of self-duality equations on a metric or on a Yang-Mills connection (for example, the Korteweg-de Vries and nonlinear Schr"odinger equations are reductions of the self-dual Yang-Mills equation). This book explores in detail the connections between self-duality and integrability, and also the application of twistor techniques to integrable systems. It has two central themes: first, that the symmetries of self-duality equations provide a natural classification scheme for integrable systems; and second that twistor theory provides a uniform geometric framework for the study of B"acklund tranformations, the inverse scattering method, and other such general constructions of integrability theory, and that it elucidates the connections between them.

Spinors, Twistors and Clifford Algebras and Quantum Deformations (Fundamental Theories of Physics)

Average customer rating:

Spinors, Twistors and Clifford Algebras and Quantum Deformations (Fundamental Theories of Physics)

Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books

General | Physics | Science | Subjects | Books

Mathematical Physics | Physics | Science | 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: 0792322517

Book Description

This volume contains the lectures given at the Second Max Born Symposium held near Wroclaw in Poland in September 1992.
The various authoritative contributions provide an excellent review of recent developments in the field and embrace the following topics: spin structures; the interrelations between Cartan's and Chevalley's theory of spinors, Clifford algebras and particle models; the interrelations between twistors, supersymmetry and phase spaces; quantum deformations; noncommutative Hopf algebras; noncommutative calculus and its applications in electrodynamics and in gauge theory; and deformed Clifford algebras and Z ₃-graded algebras.
For researchers and graduate students in mathematical and theoretical physics.

Twistor Theory (Lecture Notes in Pure and Applied Mathematics)

Average customer rating:

Twistor Theory (Lecture Notes in Pure and Applied Mathematics)

Manufacturer: CRC
ProductGroup: Book
Binding: Paperback

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

General | Physics | Science | Subjects | Books

Book Description

Presents the proceedings of the recently held conference at the University of Plymouth. Papers describe recent work by leading researchers in twistor theory and cover a wide range of subjects, including conformal invariants, integral transforms, Einstein equations, anti-self-dual Riemannian 4-manifolds, deformation theory, 4-dimensional conformal structures, and more.;The book is intended for complex geometers and analysts, theoretical physicists, and graduate students in complex analysis, complex differential geometry, and mathematical physics.

Books:

Books Index

Books Home

Recommended Books