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Wednesday, May 21, 2014

Analytical and Numerical Approaches to Mathematical Relativity - Frauendiener J., Giulini D.J.W., Perlick V.


General relativity ranks among the most accurately tested fundamental theories in all of physics. Deficiencies in mathematical and conceptual understanding still exist, hampering further progress. This book collects 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.

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Greiner W. Classical Mechanics. Systems of Particles and Hamiltonian Dynamics (2nd., Spriner, 2009)


More than a generation of German-speaking students around the world have worked their way to an understanding and appreciation of the power and beauty of modernt- oretical physics—with mathematics, the most fundamental of sciences—using Walter Greiner’s textbooks as their guide. The idea of developing a coherent, complete presentation of an entire eld of s- ence in a series of closely related textbooks is not a new one. Many older physicians remember with real pleasure their sense of adventure and discovery as they worked their ways through the classic series by Sommerfeld, by Planck, and by Landau and Lifshitz. From the students’ viewpoint, there are a great many obvious advantages to be gained through the use of consistent notation, logical ordering of topics, and - herence of presentation; beyond this, the complete coverage of the science provides a unique opportunity for the author to convey his personal enthusiasm and love for his subject. These volumes on classical physics, nally available in English, complement Greiner’s texts on quantum physics, most of which have been available to Engli- speaking audiences for some time. The complete set of books will thus provide a coherent view of physics that includes, in classical physics, thermodynamics and s- tistical mechanics, classical dynamics, electromagnetism, and general relativity; and in quantum physics, quantummechanics,symmetries, relativistic quantum mechanics, quantum electro- and chromodynamics, and the gauge theory of weak interactions.

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Greiner W., Mueller B. Gauge Theory of Weak Interactions (4ed., Springer, 2009)


"Gauge Theory of Weak Interactions" treats the unification of electromagnetic and weak interactions and considers related phenomena. First, the Fermi theory of beta decay is presented, followed by a discussion of parity violation, clarifying the importance of symmetries. Then the concept of a spontaneously broken gauge theory is introduced, and all necessary mathematical tools are carefully developed. The "standard model" of unified electroweak interactions is thoroughly discussed including current developments. The final chapter contains an introduction to unified theories of strong and electroweak interactions. Numerous solved examples and problems make this volume uniquely suited as a text for an advanced course. This fourth edition has been carefully revised.

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Practical Relativity: From First Principles to the Theory of Gravity - Richard N. Henriksen


The book is intended to serve as lecture material for courses on relativity at undergraduate level. Although there has been much written on special relativity the present book will emphasize the real applications of relativity. In addition, it will be physically designed with the use of box summaries so as to allow easy access of practical results. The book will be composed of eight chapters. Chapter 1 will give an introduction to special relativity that is the world without gravity. Implications will be presented with emphasis on time dilation and the Doppler shift as practical considerations. In Chapter 2, the four-vector representation of events will be introduced. The bulk of this chapter will deal with flat space dynamics. This will require the generalization of Newton's first and second laws. Some important astronomical applications will be discussed in Chapter 3 and in Chapter 4 some engineering applications of special relativity such as atomic clocks will be presented. Chapter 5 will be dedicated to the thorny question of gravity. The physical motivation of the theory must be examined and the geometrical interpretation presented. Chapter 6 will present astronomical applications of relativistic gravity. These include the usual solar system tests; light bending, time delay, gravitational red-shift, precession of Keplerian orbits. Chapter 7 will be dedicated to relativistic cosmology. Many of the standard cosmological concepts will be introduced, being mathematically simple but conceptually subtle. The concluding chapter will be largely dedicated to the global positioning system as an engineering problem that requires both inertial and gravitational relativity. The large interferometers designed as gravitational wave telescopes will be discussed here.

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Space-Time, Relativity, and Cosmology Hardcover by Jose Wudka


Space-Time, Relativity, and Cosmology provides a historical introduction to modern relativistic cosmology and traces its historical roots and evolution from antiquity to Einstein. The topics are presented in a non-mathematical manner, with the emphasis on the ideas that underlie each theory rather than their detailed quantitative consequences. A significant part of the book focuses on the Special and General theories of relativity. The tests and experimental evidence supporting the theories are explained together with their predictions and their confirmation. Other topics include a discussion of modern relativistic cosmology, the consequences of Hubble's observations leading to the Big Bang hypothesis, and an overview of the most exciting research topics in relativistic cosmology. This textbook is intended for introductory undergraduate courses on the foundations of modern physics. It is also accessible to advanced high school students, as well as non-science majors who are concerned with science issues.

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100 Great Problems of Elementary Mathematics - by Heinrich Dorrie



Problems that beset Archimedes, Newton, Euler, Cauchy, Gauss, Monge and other greats, ready to challenge today's would-be problem solvers. Among them: How is a sundial constructed? How can you calculate the logarithm of a given number without the use of logarithm table? No advanced math is required. Includes 100 problems with proofs.


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Solved Problems in Lagrangian and Hamiltonian Mechanics (Grenoble Sciences) Claude Gignoux



The aim of this work is to bridge the gap between the well-known Newtonian mechanics and the studies on chaos, ordinarily reserved to experts. Several topics are treated: Lagrangian, Hamiltonian and Jacobi formalisms, studies of integrable and quasi-integrable systems. The chapter devoted to chaos also enables a simple presentation of the KAM theorem. All the important notions are recalled in summaries of the lectures. They are illustrated by many original problems, stemming from real-life situations, the solutions of which are worked out in great detail for the benefit of the reader.
This book will be of interest to undergraduate students as well as others whose work involves mechanics, physics and engineering in general.


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Tuesday, May 20, 2014

Einstein A. Relativity. The special and the general theory (Pi Press, 2005)

Robert Geroch builds on Einstein's work with commentary that addresses the ideas at the heart of the theory, bringing a modern understanding of relativity to the text. He elucidates how special relativity is a reconciliation of the contradictions between the nature of light and the principle of relativity; he expands on Einstein's treatment of the geometry of space-time and the fundamental notion of an "event"; he explains in detail, but without technical language, the equivalence of inertial and gravitational mass, a cornerstone of general relativity.


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The Genesis of Feynman Diagrams by A. Wuethrich



In a detailed reconstruction of the genesis of Feynman diagrams the author reveals that their development was constantly driven by the attempt to resolve fundamental problems concerning the uninterpretable infinities that arose in quantum as well as classical theories of electrodynamic phenomena. Accordingly, as a comparison with the graphical representations that were in use before Feynman diagrams shows, the resulting theory of quantum electrodynamics, featuring Feynman diagrams, differed significantly from earlier versions of the theory in the way in which the relevant phenomena were conceptualized and modelled. The author traces the development of Feynman diagrams from Feynman's "struggle with the Dirac equation" in unpublished manuscripts to the two of Freeman Dyson's publications which put Feynman diagrams into a field theoretic context. The author brings to the fore that Feynman and Dyson not only created a powerful computational device but, above all, a new conceptual framework in which the uninterpretable infinities that had arisen in the old form of the theory could be precisely identified and subsequently removed in a justifiable manner.
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Group Theory in Physics Problems and Solutions - Michael Aivazis


Though the product description does not explicitly say it, this book is a collection of the end-of-chapter problems in Group Theory in Physics with solutions. Consequently, the problems make frequent references to definitions, axioms, and theorems in Group Theory in Physics, and the solutions follow its notation. This limits the usefulness of this book unless you own the other one also. Instructors usingGroup Theory in Physics as a textbook should be aware of the existence of this book since using the end-of-chapter problems as homework would be pointless.


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