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Introduction to String Field Theory
Introduction to String Field Theory (Advanced Series in Mathematical Physics, Vol 8)
By Warren Siegel
Publisher: World Scientific Pub Co Inc
Number Of Pages: 256
Publication Date: 1989-01
Sales Rank: 3188314
ISBN / ASIN: 9971507315
EAN: 9789971507312
Binding: Hardcover
Manufacturer: World Scientific Pub Co Inc
Studio: World Scientific Pub Co Inc
Average Rating: 3
Total Reviews: 1
Review:
Very dense but good for the time
The author introduces the subject of his book as "the newest approach" to string theory, which he defines in analogy to the point particle theory, as an approach to the calculation of relevant quantities using field theory Lagrangians, instead of "off-shell" S-matrix computations, and which is done in 10 dimensions. The first five chapters of the book is not concerned directly with strings at all, but with the quantization of gauge theories, both pure and with the presence of matter (fermions). The author considers first point particle fields in the light cone gauge. In this gauge the field theory appears nonrelativistic, satisfying a non-relativistic "Schrodinger equation" with an imaginary Hamiltonian. The author then discusses the Yang-Mills theory in the light cone gauge, and derives the free Lagrangian for this theory. This motivates a detailed discussion of the conformal algebra since (nonlinear) representations of the Poincare group model the kinetic term of a free light-cone field theory, and one can obtain these, as the author shows, using the conformal group. He later generalizes to the case where interactions are present, and derives the Feynman rules. The reader can readily see the tension between the demands for covariance and unitarity, that is characteristic of gauge theories. The light-cone gauge is manifestly covariant, but in two less dimensions than the dimension of spacetime the fields are formulated in. This is apparent in the use of the Poincare group ISO(D-1,1), the representations of which are constructed for arbitrary massless and massive theories. The representations are nonlinear in the coordinates, and are constructed from irreducible representations of the SO(D-2) rotation group of the SO(D-1,1) Lorentz group. The conformal group is then SO(D, 2).
In these initial five chapters the reader also gets a detailed overview of the BRST formalism, which is very important in the quantization of gauge theories. This formalism is first introduced in the context of the Hamiltonian formalism, which is manifestly covariant in D - 1 dimensions. This involves as expected a separation of coordinates into space and time with the time components of the gauge fields set to zero. The famous Faddeev-Popov ghosts make their appearance here, since the quantization problem is a problem with constraints. The author gives several reasons for using the BRST formalism, and the reader sees the origin of the Slavnov-Identities, which are generalizations of the amazing Ward identities and are a consequence of the side constraint of unitarity.
The actual consideration of strings first takes place in chapter 6. The large amount of work done by the author in the first five chapters to find a general Poincare- and gauge-invariant action for any collection of fields is finally applied in this chapter and the rest of the book. The idea of viewing strings as 2-dimensional field theories is the main point behind the author's approach. The author quantizes the bosonic string in the light-cone gauge and derives the Poincare algebra, which can be viewed as a specialization of what was done in the first two chapters. This is generalized immediately to the case to the fermionic case by introducing a 2D supersymmetry on the world sheet, in complete analogy with the point particle case in chapter five. In this discussion the reader can see clearly the origin of the requirement that D be equal to 10. A manifestly covariant formalism is then discussed, which is a generalization of the bosonic string and the superparticle of chapter 5. This discussion is interesting in that it shows the origin of the Kac-Moody algebra in the covariant derivatives, and the Virasoro algebra. The BRST formalism is discussed later in the context of the first-quantization of the bosonic string as a constrained problem in the conformal gauge. The Feynman rules for interacting strings are then derived using first the external field formalism, and then using functional integration.
The author gets down to studying string field theory in the context of what was done early in chapter 2 in chapters 10 and 11, namely the light-cone gauge and the BRST formalism, with the goal to include the contributions of the string interactions. As expected, in the free field case the bosonic open strings satisfy a Schroedinger-like equation, and interactions are described by splitting and joining of strings, and as expected from a field-theoretic point of view, the graphs are composed of vertices and propagators. The BRST formalism is done only for the closed string case.The author introduces the reader to how to construct gauge-invariant actions for interacting strings in the last chapter of the book. He is careful to note that a string field theory of interacting strings does not exist, and gives explanations to the difficulties involved in constructing such theories. I have not followed the research on this topic since this book was published, so cannot comment on the present state of atttempts to construct these theories, except for those attempts to give an interpretation of open and closed strings in terms of algebraic topology, C*-algebras, and K-theory. These however do not permit any kind of Feynman rules to be derived. No doubt a perusal of the preprint servers will reveal that this problem has been absorbed in the current emphasis on D-brane and M-theories.
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Methods for Solving Mathematical Physics Problems
V. I. Agoshkov, P. B. Dubovski , V. P. Shutyaev, "Methods for Solving Mathematical Physics Problems"
Cambridge International Science Publishing; New Ed edition (October 1, 2006) | ISBN:1904602053 | 328 pages | PDF | 2,5 Mb
The aim of the book is to present to a wide range of readers (students, postgraduates, scientists, engineers, etc.) basic information on one of the directions of mathematics, methods for solving mathematical physics problems. The authors have tried to select for the book methods that have become classical and generally accepted. However, some of the current versions of these methods may be missing from the book because they require special knowledge. The book is of the handbook-teaching type. On the one hand, the book describes the main definitions, the concepts of the examined methods and approaches used in them, and also the results and claims obtained in every specific case. On the other hand, proofs of the majority of these results are not presented and they are given only in the simplest (methodological) cases. Another special feature of the book is the inclusion of many examples of application of the methods for solving specific mathematical physics problems of applied nature used in various areas of science and social activity, such as power engineering, environmental protection, hydrodynamics, elasticity theory, etc. This should provide additional information on possible applications of these methods. To provide complete information, the book includes a chapter dealing with the main problems of mathematical physics, together with the results obtained in functional analysis and boundary-value theory for equations with partial derivatives.
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Contemporary Aspects of Complex Analysis, Differential Geometry And Mathematical Phys
Stancho Dimiev, Kouei Sekigawa, "Contemporary Aspects of Complex Analysis, Differential Geometry And Mathematical Physics "
World Scientific Publishing Company (July 30, 2005) | ISBN-10: 9812563903 | 360 pages | PDF | 15,7 Mb
This volume presents the cutting-edge contributions to the Seventh International Workshop on Complex Structures and Vector Fields, which was organized as a continuation of the high successful preceding workshops on similar research.
The volume includes works treating ambitious topics in differential geometry, mathematical physics and technology such as Bézier curves in space forms, potential and catastrophy of a soap film, computer-assisted studies of logistic maps, and robotics.
Contents:
Geodesics and Trajectories for Kähler Magnetic Fields (T Adachi)
Stable Simply Connected Minimal Surfaces in RN and SO(N, C)-Action (N Ejiri)
On a Fibre Bundle Formulation of Classical and Statistical Mechanics (B Iliev)
Canonical Metrics and Harder–Narasimhan Filtration (J Keller)
Type-Changing Transformations of Hurwitz Pairs, Quasiregular Functions, and Hyper-Kählerian Holomorphic Chains II (J Lawrynowicz et al.)
A Quaternion Approach in Physics and Engineering Calculation (V Markova & V Shopov)
On the Complex WKB Analysis for a 2nd Order ODE with the Most General Characteristic Polygon (M Nakano)
Kinematics and Vectorfields on Differentiable Spaces (K Spallek)
and other papers
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Tales of Physicists and Mathematicians
Tales of Physicists and Mathematicians
Simon Gindikin, Tales of Physicists and Mathematicians second edition
Springer | ISBN 0387360263 | 2007 | PDF | 2 MB | 394 pages
This revised and greatly expanded second edition of the classic Russian text "Tales of Mathematicians and Physicists" contains a wealth of new information about the lives and accomplishments of more than a dozen scientists throughout history. Included are individuals from the late nineteenth century: Klein, Poincaré, Ramanujan, and Penrose, as well as renowned figures from earlier eras, such as Leibniz, Euler, Lagrange, and Laplace. A unique mixture of mathematics, physics, and history, this volume provides biographical glimpses of scientists and their contributions in the context of the social and political background of their times.
The author examines many original sources, from the scientists’ research papers to their personal documents and letters to friends and family; furthermore, detailed mathematical arguments and diagrams are supplied to help explain some of the most significant discoveries in calculus, celestial mechanics, number theory, and modern relativity. What emerges are intriguing, multifaceted studies of a number of remarkable intellectuals and their scientific legacy.
Written by a distinguished mathematician and accessible to readers at all levels, this book is a wonderful resource for both students and teachers and a welcome pleasant journey to the history of science.
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New Optimization Algorithms in Physics
New Optimization Algorithms in Physics
9783527404063 | (3527404066) | John Wiley & Sons | 2004 | 6 MB | RS
Many physicists are not aware of the fact that they can solve their problems by applying optimization algorithms. Since the number of such algorithms is steadily increasing, many new algorithms have not been presented comprehensively until now. This presentation of recently developed algorithms applied in physics, including demonstrations of how they work and related results, aims to encourage their application, and as such the algorithms selected cover concepts and methods from statistical physics to optimization problems emerging in theoretical computer science.
Optimization problems occur very frequently in physics. Some of them are easy to handle with conventional methods also used in other areas such as economy or operations research. But as soon as a huge number of degrees of freedom are involved, as is typically the case in statistical physics, condensed matter, astrophysics and biophysics, conventional methods fail to find the optimum in a reasonable time and new methods have to be invented. This book contains a representative collection of new optimization algorithms that have been devised by physicists from various fields, sometimes based on methods developed by computer scientists and mathematicians. However, it is not a mere collection of algorithms but tries to demonstrates their scope and efficiency by describing typical situations in physics where they are useful.
The individual articles of this collections are self-contained and should be understandable for scientists routinely using numerical tools. A more basic and pedagogical introduction into optimization algorithms is our book on Optimization Algorithms in Physics, which can serve as an appendix for the newcomer to this field of computational physics or for undergraduate students. The reason why we found it necessary to compose another book in this field with a greater focus is the fact that the application of optimization methods is one of the strongest growing fields in physics. The main reasons for these current developments are the following key factors:
First of all great progress has been made in the development of new combinatorial optimization methods in computer science. Using these sophisticated approaches, much larger system sizes of the corresponding physical systems can be treated. For many models the systems sizes which were accessible before, were too small to obtain reliable and significant data. However, this is now possible. In this way computer science has helped physics. But knowledge transfer also works the other way round. Physics provides still new insights and methods of treating optimization problems, such as the earlier invention of the simulated annealing technique. Recent algorithmic developments in physics are, e.g., the extremal optimization method or the hysteric optimization approach, both covered in this book.
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Analytical and Numerical Approaches to Mathematical Relativity
Jörg Frauendiener (Editor), Domenico J.W. Giulini (Editor), Volker Perlick (Editor),
\"Analytical and Numerical Approaches to Mathematical Relativity (Lecture Notes in Physics)\"
Springer | ISBN / ASIN: 3540310274 | 2006 | 279 pages | PDF | 2.8MB
Today, general relativity rates among the most accurately tested fundamental theories in all of physics. However, deficiencies in our mathematical and conceptual understanding still exist, and these partly hamper further progress. For this reason alone, but no less important from the point of view that a theory-based prediction should be regarded as no better than one's own structural understanding of the underlying theory, one should undertake serious investigations into the corresponding mathematical issues. This book contains a representative collection of surveys by experts in mathematical relativity writing about the current status of, and problems in, their fields. There are four contributions for each of the following mathematical areas: differential geometry and differential topology, analytical methods and differential equations, and numerical methods. This book addresses graduate students and specialist researchers alike.
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Explorations in Mathematical Physics: The Concepts Behind an Elegant Language
Publisher: Springer
Number Of Pages: 544
Publication Date: 2006-09-15
Sales Rank: 257300
ISBN / ASIN: 0387309438
EAN: 9780387309439
Binding: Hardcover
Manufacturer: Springer
Studio: Springer
Average Rating: 4
Total Reviews: 1
Quote:
Book Description:
Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature?
This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You'll see how the accelerated frames of special relativity tell us about gravity. On the journey, you'll discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology.
The book takes a fresh approach to tensor analysis built solely on the metric and vectors, with no need for one-forms. This gives a much more geometrical and intuitive insight into vector and tensor calculus, together with general relativity, than do traditional, more abstract methods.
Don Koks is a physicist at the Defence Science and Technology Organisation in Adelaide, Australia. His doctorate in quantum cosmology was obtained from the Department of Physics and Mathematical Physics at Adelaide University. Prior work at the University of Auckland specialised in applied accelerator physics, along with pure and applied mathematics.
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Operator Theory, Analysis and Mathematical Physics
Operator Theory, Analysis and Mathematical Physics (Operator Theory: Advances and Applications)
Publisher:Birkhäuser Basel (2007-04-19) | ISBN-10: 3764381345 | PDF | 7.3 Mb | 257 pages
This volume contains lectures delivered by the participants of the International Conference Operator Theory and its Applications in Mathematical Physics (OTAMP 2004), held at the Mathematical Research and Conference Center in Bedlewo near Poznan, Poland. The idea behind these lectures was to present interesting ramifications of operator methods in current research of mathematical physics. The main topics are functional models of non-selfadjoint operators, spectral properties of Dirac and Jacobi matrices, Dirichlet-to-Neumann techniques, Lyapunov exponents methods, and inverse spectral problems for quantum graphs.
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Geometric Algebra for Physicists
Geometric Algebra for Physicists
Publisher:Cambridge University Press(2003-07-07) | ISBN-10: 0521480221 | PDF | 3.3 Mb | 592 pages
As leading experts in geometric algebra, Chris Doran and Anthony Lasenby have led many new developments in the field over the last ten years. 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, the volume is also a valuable reference for researchers working in the fields of relativity and quantum theory.
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Magnetic Monopoles (Theoretical and Mathematical Physics
)
Magnetic Monopoles (Theoretical and Mathematical Physics)
Springer | ISBN 3540252770 | 2005-09-29 | DJVU |532 pages |3.92 MB
This monograph addresses the field theoretical aspects of magnetic monopoles. Written for graduate students as well as researchers, the author demonstrates the interplay between mathematics and physics. He delves into details as necessary and develops many techniques that find applications in modern theoretical physics. This introduction to the basic ideas used for the description and construction of monopoles is also the first coherent presentation of the concept of magnetic monopoles. It arises in many different contexts in modern theoretical physics, from classical mechanics and electrodynamics to multidimensional branes. The book summarizes the present status of the theory and gives an extensive but carefully selected bibliography on the subject. The first part deals with the Dirac monopole, followed in part two by the monopole in non-abelian gauge theories. The third part is devoted to monopoles in supersymmetric Yang-Mills theories.
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