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Few people studying Gauge Field Theory need to be convinced ofthe importance of the work of 't Hooft. This volume contains aselection of articles and review topics covering his well-knownstudies on the renormalization of non-Abelian gauge theorems,topological phenomena in gauge field theory and thoughts on the roleof black holes in quantum gravity.
The chapters are tied together bythoughtful commentaries which provide a background and theillumination of hindsight - together they form a clear and coherentpicture of the physical and theoretical importance of gauge theoriesand the gauge principle. This book is ideal for students andresearchers.
Gerard 't Hooft is Professor of Theoretical Physics atthe University of Utrecht, The Netherlands. He has taught at Harvard,SLAC and Caltech prior to his present position. Other distinguishedhonors include being awarded the Dannie Heineman Prize, the HonoraryDoctorate of Science from the University of Chicago, Wolf Prize of theState of Israel, Pius XI Medal (Vatican), and the Lorentz Medal (KNAW,Amsterdam). ... Read more

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Mathematical Physics: Advanced Topics is the second of a two-volume set designed for senior undergraduate and postgraduate students. The author provides detailed discussion of topics including partial differential equations, ordinary differential equations, special functions including gamma, beta and Bessel functions, classical orthogonal polynomials, spherical harmonics, generalized functions, the Dirac-delta function, Fourier transforms, group theory, eigenvalues, eigenvectors, matrix representations and diagonalization of matrices, complex variables, analytic functions, Taylor and Laurent series, contour integrals, residue theorem and applications, and method of steepest descent. ... Read more

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Building on the material learned by students in their first few years of study, this book presents an advanced level course on statistical and thermal physics. It begins with a review of the formal structure of statistical mechanics and thermodynamics considered from a unified viewpoint. After a brief revision of non-interacting systems, emphasis is laid on interacting systems. First, weakly interacting systems are considered, where the interest is in seeing how such interactions cause small deviations from the non-interacting case. Second, systems are examined where interactions lead to drastic changes, namely phase transitions. A number of specific examples are given, and these are unified within the Landau theory of phase transitions. The final chapter of the book looks at non-equilibrium systems and the way these evolve towards equilibrium. Here, fluctuations play a vital role, as is formalized in the Fluctuation–Dissipation theorem. ... Read more

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A good supplement to standard SM textbooks
I used this book to enrich the examples in my lecture notes for statistical mechanics. It covers all topics in the standrad course for statistical mechanics, from thermodynamics to basics of non-equilibrium statistical mechanics. The author provides many examples to illusrate the theory. The style of presentation, especially, the mathematics, is not so formal like the one by K. Huang and is very readable. In my opinion, it is a useful referrence to students and teachers for the course of statistical mechanics. ... Read more

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Focuses on the state of the art of Monte Carlo methods in radiation physics and particle transport simulation and applications. Proceedings of the Monte Carlo 2000 Conference, held in Lisbon, October 23-26,2000. ... Read more

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This book presents information in an accessible format and easily manageable sections. Broadens knowledge by presenting science in context, with a strong emphasis on economic, social and environmental issues. It encourages interactive learning through a range of methods including investigations, data handling, exercises and questions throughout the text. There is new, increased coverage of communication and transport. It prepares students for the examinations with examination questions with answers, help and advice. ... Read more

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These Biology revision notes provide examiner's tips on how to gain extra marks in the exam and aim to cover the core content of all major syllabuses in an accessible way. ... Read more

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Student-friendly presentation of key concepts.Interactive format enables students to test themselves throughout.Contains valuable worked examples.All answers are provided so that the book can be used for self-study or as part of a taught course. ... Read more

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The Advanced Level specifications for courses starting in September 2000 divide the content into AS material, which will normally be covered in the first year, and A2 material, which will normally be covered in the second year. This text covers the AS material for Physics. To help students make the transition from GCSE Double Award Science each topic starts at the level required for a Grade C pass at GCSE, building up gradually to the depth of coverage required for AS. The key skills of communication, information technology and application of number are specifically covered through questions and activities at the end of each chapter although there are further opportunities to develop these skills throughout. ... Read more

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great book
has a lot of information, is clear, has good headings.... great book overall ... Read more

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A good introduction to the early work
The finding of invariants for knots has been a major unsolved problem in mathematics for over 125 years. The difficulty of the problem is attested to by the paucity of results over decades of time in the early 20th century. Then in the 1980's Vaughn Jones discovered some invariants that are related to ideas in physics, namely the theory of integrable models in statistical mechanics. This book is a collection of articles discussing the Jones work and other approaches that relate knot theory and statistical mechanics, written a few years after his discovery. My review will be confined to the articles which I read in detail.

An article by Vaughn Jones begins the book and discusses the connection between subfactors of von Neumann algebras and statistical mechanics. These von Neumann algebras occur as algebras of transfer matrices in statistical mechanics. These transfer matrices satisfy algebraic relations that are essentially the same as those appearing in special types of von Neumann algebras. The author makes it a point to discuss in detail the relevant constructions of von Neumann algebras, believing this has not been done in the literature. The von Neumann algebras related to the transfer matrices are particular types of II(1) and III factors, which the author constructs using Bratteli diagrams and the Gelfand-Naimark-Segal construction.

The article by Louis Kauffman discusses polynomial invariants of knots and the Yang-Baxter factorization equation. Polynomial invariants based on the Yang-Baxter equations are one-variable polynomials. The author points out that it is unknown whether two-variable invariants can be extracted from the Yang-Baxter equations, but points out how to construct these using skein models.

The article by Michio Jimbo is an introduction to the Yang-Baxter equation with emphasis on the role of quantum groups. The solutions of the Yang-Baxter equation are discussed in the light of the work of A. Belavin and V.G. Drinfeld in the context of simple Lie algebras. The author shows in this case that the solutions are either elliptic, trigonometric, or rational functions. This is followed by a discussion of how to "quantize" this situation, which leads to the theory of quantum groups, a field that has grown considerably since this article was written. The author discusses a particular example of a quantum group, called the universal enveloping algebra, and studies its representations and the Drinfeld universal R matrix. The "classical" Yang-Baxter r-matrix is then the classical limit of this R-matrix. The author shows how to obtain higher representations by using an analog of the technique of constructing irreducible representations of Lie algebras by forming tensor products of fundamental representations and decomposing them. This technique is known as the fusion procedure here and elsewhere in the literature.

The article by Toshitake Kohno is a review article on representations of the braid group with respect to the Yang-Baxter equation for face models in statistical mechanics. The representations of the braid group appear explicitly as the monodromy of integrable connections defined for any simple Lie algebra and its irreducible representation. Interestingly, the connections describe n-point functions in a conformal field theory on the Riemann sphere with gauge symmetry. The author begins with a finite-dimensional complex simple Lie algebra and its irreducible representation. Selecting an orthonormal basis of this Lie algebra with respect to the Cartan-Killing form, the author constructs certain matrices in the endomorphisms of the n-fold tensor product of the representation. These matrices satisfy certain relations that are a special case of the Yang-Baxter equation. A connection defined using these matrices and a complex parameter ranging over a set consisting complex n-vectors with unequal coordinates is shown to be integrable using these relations. The fundamental group of the complex parameter set is the 'pure braid group with n strings' and the (quadratic) relations are viewed as an infinitesimal version of the defining relations of the pure braid group. By taking the quotient of the parameter set with the symmetric group one obtains the braid group, the representations of which are consequently obtained using the monodromy of this connection. Another representation is derived from the quantized universal enveloping algebra of the Lie algebra.

By far the most interesting article, and the one least rigorous mathematically, is the one by Edward Witten on quantum field theory and the Jones polynomial. The author shows that a Yang-Mills theory in 2 + 1 dimensions consisting of merely the Chern-Simons terms is exactly soluble and can be used to give the Jones polynomial a three-dimensional interpretation, which was highly desired at the time of writing. He also shows that the Jones polynomial can be generalized from the 3-sphere to arbitrary 3-manifolds, and gives invariants for these manifolds, which can be computed from a surgery presentation. The author's constructions are fascinating, particularly from a physics standpoint, but mathematically they are very suspect, since they are dependent on the notion of a path integral. The latter, despite decades of concentrated effort, has defied a mathematically rigorous formulation. The results in the article have thus been classified as "physical mathematics", and therefore conjectural and tentative from a purely mathematical standpoint. This is a fair classification, and it motivated other mathematicians to find alternative formulations that are well-defined mathematically. Indeed, this article has resulted in an explosion of research on both knot invariants and invariants for 3-manifolds, some of which has remain tied to quantum field theory, and some making a concentrated effort to remove these invariants from their dependence on it. ... Read more

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Optical microcavities are structures that enable confinement of light to microscale volumes. The universal importance of these structures has made them indispensable to a wide range of fields. This important book describes the many applications and the related physics, providing both a review and a tutorial of key subjects by leading researchers from each field. The topics include cavity QED and quantum information, nanophotonics and nanostructure interactions, wavelength switching and modulation in optical communications, optical chaos and biosensors. ... Read more

Customer Reviews (2)

i want to review but...
im a maths student in turkey and i really want to find this book,but here it is impossible to find it! i will be glad to the person who can help me finding the book please contact me from my e-mail... THANX

Very Practical for Application!
I was trying to prove that two Banach Spaces have bounded linear transformation T implies T* is continuous from Y* to X* in their weak* topology. It requires two pairs of additions and the property of BanachSpace. Thanks to this book I didn't miss the shot. This book is typicalRussian style -straight forward and no BS! I learn many from this book. Ihope Dover can pick this book and print it for students. German math bookstend to use wired symbles. American textbooks tend to have more exercisesthan examples. You will never pick up enough tools to tackle exercises byAmerican textbooks. ... Read more

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Further Advanced Physics" covers the A2 modules and builds on the content of "Introduction to Advanced Physics", covering AS. It also contains 8 synoptic chapters which draw together ideas from the whole of the physics course. These can be used to prepare students for the synoptic assessment. Key skills of communication, information technology and application of number are covered throughout, and there are specific skills tasks at the end of each chapter. There are also questions from recent past papers. ... Read more

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Providing a view of research in a broad area of mathematical physics, this volume presents a collection of works by leading figures in the field. It celebrates Elliot H. Lieb's contribution to the subject and offers a glimpse into the life and work-style of Lieb and some of his contemporaries. ... Read more