Book Description
This new edition embraces the whole continent from both national and regional perspectives, and combines political survey with grass roots 'people' history. Asa Briggs (The Lord of Lewes) and Patricia Clavin, have written a comprehensive and accessible book covering the whole of Europe from the French Revolution to the present day. completely revised and brought up-to-date, the authors use a very broad range of sources including memoirs, archives, letters, songs and newspapers. Several areas have been updated specifically for this edition including religion and the modern Papacy, immigration in Europe and relationships between minority and majority groups, UNESCO, the European Bill of Rights, seeds of conflict in Bosnia and Croatia and Europe's relations with the wider world, with particular attention to the Middle East and Japan. For readers interested in European history.
Book Description
Theodore Frankel explains those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms essential to a better understanding of classical and modern physics and engineering. Key highlights of his new edition are the inclusion of three new appendices that cover symmetries, quarks, and meson masses; representations and hyperelastic bodies; and orbits and Morse-Bott Theory in compact Lie groups. Geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space. First Edition Hb (1997): 0-521-38334-X First Edition Pb (1999): 0-521-38753-1
Customer Reviews:
Fantastic - for the scientist.......2007-07-18
A very good book: buy it. But only if you are a scientist or student of physics/mathematics. This is not popular-science-common-public level.
a book worth keeping.......2007-05-01
This book can be quite confusing if you start without any background on the idea of manifold or knows nothing about general relativity. However, it does have strong points:
1. The notation is very up-to-date, and is entirely coordinate-independant approach.
2. The author explains in great details of formulation of modern differential geometry, and the details are comparatively lacking in other reference books.
3. The author never hesitate to use graphs and diagrams to illustrate points, and stroke nice balance in between mathematics rigor and physical insight.
Although it appears quite verbose at some point, it is mainly because differential geometry is such a heavy subject. Another book nice to have as companion reading is Goldburg's "Tensor analysis on Manifold", a terse, well-written text book.
Phenomenal .......2006-11-13
I just finished reading this book and I found it phenomenal. The physical ideas are made very clear in a natural mathematical framework.
You should buy this, despite its flaws.......2006-03-03
The other reviews on this page give this book anywhere from 1 to 5 stars, and they are all correct in their own way. The book is inspired, deep and full of physics applications and insights. On the other hand, it skims over mathematical rigor to a large degree and focuses more on defining things, getting a feel for them and moving on to application.
My advice: buy the book for its strengths, and read other books in parallel if you need more rigor. But still, buy it.
Also, things can be confusing on the first two or three reads, but keep at it and you will be glad you did.
The perfect first book in differential geometry.......2005-01-28
Differential geometry can be a very intimidating subject due to its heavy formalism. There are complete books (such as Kobayashi& Nomizu) very good as reference books, and there very few books that show the reader the picture behind the formulas.
This is one such book. It tells you the intuition behind each construction and from this point of view it has many things in common with Arnold's famous book on Math. Methods in Classical Mechanics. But where as Arnold does not pay too much attention to formalism, this book achieves this task as well. It shows the reader how to do those impossible computations as well.
This is definitely the first place to look at if you want to really learn differential geometry. If it seems difficult it is only because the subject is so.
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An Introduction to Dirac Operators on Manifolds
Jan Cnops
Manufacturer: Birkhäuser Boston
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ASIN: 0817642986 |
Book Description
Dirac operators play an important role in several domains of mathematics and physics, for example: index theory, elliptic pseudodifferential operators, electromagnetism, particle physics, and the representation theory of Lie groups. In this essentially self-contained work, the basic ideas underlying the concept of Dirac operators are explored. Starting with Clifford algebras and the fundamentals of differential geometry, the text focuses on two main properties, namely, conformal invariance, which determines the local behavior of the operator, and the unique continuation property dominating its global behavior. Spin groups and spinor bundles are covered, as well as the relations with their classical counterparts, orthogonal groups and Clifford bundles. The chapters on Clifford algebras and the fundamentals of differential geometry can be used as an introduction to the above topics, and are suitable for senior undergraduate and graduate students. The other chapters are also accessible at this level so that this text requires very little previous knowledge of the domains covered. The reader will benefit, however, from some knowledge of complex analysis, which gives the simplest example of a Dirac operator. More advanced readers---mathematical physicists, physicists and mathematicians from diverse areas---will appreciate the fresh approach to the theory as well as the new results on boundary value theory.
Average customer rating:
- Good support for theoretical Physics ...
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An Introduction to Geometrical Physics
R. Aldrovandi , and
J. G. Pereira
Manufacturer: World Scientific Publishing Company
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ASIN: 9810222327 |
Book Description
This book stresses the unifying power of the geometrical framework in bringing together concepts from the different areas of physics. Common underpinnings of optics, elasticity, gravitation, relativistic fields, particle mechanics and others subjects are underlined. It attempts to extricate the notion of space currently in the physical literature from the metric connotation.
The book's goal is to present mathematical ideas associated with geometrical physics in a rather introductory language. Included are many examples from elementary physics and also, for those wishing to reach a higher level of understanding, a more advanced treatment of the mathematical topics. It is aimed as an elementary text, more so than most others on the market, and is intended for first year graduate students.
Customer Reviews:
Good support for theoretical Physics ..........2002-10-24
This book contains lots of subjects all of great interest for students in theoretical Physics. The right way to read this book is just to read those chapters one is interested in. The level is at advanced-undergraduate / graduate. Tensors are treated in a self contained way, as differential forms, and connection with Physics is always present. A good way to learn more from that stuff is to couple this book with Frankel's "The Geometry of Physics" (which goes more far by treating homology, cohomology, De Rahm theorem ...). One thing one could point out is that Aldrovandi's formalism is not the most recent (compared to Frankel's) but this is just a small problem for those who are used to maths. This book is a useful reference and matemathical support for those learning on QFT and GR. I particularly appreciated the part about tensor fields, differential forms and integration of differential forms (Very well written !). Sections about chains, homology, De Rham's theorem, Betti numbers ... are also quite good. The last few chapters contain some original and interesting parts about GR compared to Gauge Theory, dS and AdS spaces, even if this section seems to me a bit shortly written. The book contains also some other stuff that you will not need immediatelly for QFT and GR (Morse theory, ...).
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.
Average customer rating:
- good for mathematical physics
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An Introduction to Differential Geometry and Topology in Mathematical Physics
Wang Rong , and
Cheng Yue
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover
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ASIN: 9810235593 |
Customer Reviews:
good for mathematical physics.......2000-04-08
This book deals with Differential Geometry and Topology for those who want to study Mathematical Physics.It covers topics from differential manifold to 4-manifolds theory. In the book I can see that the author tries to derive all the relavent formulas.However the explanation for the derivation is too brief and it seems to be hard for novice or student to follow it.(But it is not that bad if you follow only mathematics) It would be helpful to those who really are serious about geometrical or topological approach to mathematical physics.
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An Introduction to Lorentz Surfaces (De Gruyter Expositions in Mathematics)
Tilla Weinstein
Manufacturer: Walter de Gruyter
ProductGroup: Book
Binding: Library Binding
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ASIN: 311014333X |
Book Description
This book gives an introduction to modern geometry. Starting from an elementary level the author develops deep geometrical concepts, playing an important role nowadays in contemporary theoretical physics. He presents various techniques and viewpoints, thereby showing the relations between the alternative approaches.
At the end of each chapter suggestions for further reading are given to allow the reader to study the touched topics in greater detail.
This second edition of the book contains two additional more advanced geometric techniques: (1) The modern language and modern view of Algebraic Geometry and (2) Mirror Symmetry.
The book grew out of lecture courses. The presentation style is therefore similar to a lecture. Graduate students of theoretical and mathematical physics will appreciate this book as textbook. Students of mathematics who are looking for a short introduction to the various aspects of modern geometry and their interplay will also find it useful. Researchers will esteem the book as reliable reference.
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An Introduction to Spinors and Geometry With Applications in Physics
I. M. Benn , and
Robert W. Tucker
Manufacturer: Institute of Physics Publishing
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Binding: Hardcover
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ASIN: 0852741693 |
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An Introduction to Noncommutative Spaces and Their Geometries (Lecture Notes in Physics)
Giovanni Landi
Manufacturer: Springer
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ASIN: 3540635092 |
Book Description
These notes arose from a series of introductory seminars on noncommutative geometry the author gave at the University of Trieste. They are mainly an introduction to Connes' noncommutative geometry and could serve as a "first aid kit" before one ventures into the beautiful but bewildering landscape of Connes' theory. The main difference with other available introductions to Connes' work is the emphasis on noncommutative spaces seen as concrete spaces. Important examples of noncommutative spaces are provided by noncommutative lattices. The latter are subject of intensive work the author is doing in collaboration with others. These notes are also meant to be an introduction to these researches.
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