The Mathematical Structure Of Classical And Relativistic Physics

Author : Enzo Tonti
Publisher : Springer Science & Business Media
ISBN 13 : 1461474221
Total Pages : 537 pages
Book Rating : 4.27/5 ( download)

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Download or read book The Mathematical Structure of Classical and Relativistic Physics written by Enzo Tonti and published by Springer Science & Business Media. This book was released on 2013-09-07 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theories describing seemingly unrelated areas of physics have surprising analogies that have aroused the curiosity of scientists and motivated efforts to identify reasons for their existence. Comparative study of physical theories has revealed the presence of a common topological and geometric structure. The Mathematical Structure of Classical and Relativistic Physics is the first book to analyze this structure in depth, thereby exposing the relationship between (a) global physical variables and (b) space and time elements such as points, lines, surfaces, instants, and intervals. Combining this relationship with the inner and outer orientation of space and time allows one to construct a classification diagram for variables, equations, and other theoretical characteristics. The book is divided into three parts. The first introduces the framework for the above-mentioned classification, methodically developing a geometric and topological formulation applicable to all physical laws and properties; the second applies this formulation to a detailed study of particle dynamics, electromagnetism, deformable solids, fluid dynamics, heat conduction, and gravitation. The third part further analyses the general structure of the classification diagram for variables and equations of physical theories. Suitable for a diverse audience of physicists, engineers, and mathematicians, The Mathematical Structure of Classical and Relativistic Physics offers a valuable resource for studying the physical world. Written at a level accessible to graduate and advanced undergraduate students in mathematical physics, the book can be used as a research monograph across various areas of physics, engineering and mathematics, and as a supplemental text for a broad range of upper-level scientific coursework.

Author : Antonio Romano
Publisher : Springer Nature
ISBN 13 : 3030272370
Total Pages : 496 pages
Book Rating : 4.71/5 ( download)

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Download or read book The Physical and Mathematical Foundations of the Theory of Relativity written by Antonio Romano and published by Springer Nature. This book was released on 2019-09-25 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique textbook offers a mathematically rigorous presentation of the theory of relativity, emphasizing the need for a critical analysis of the foundations of general relativity in order to best study the theory and its implications. The transitions from classical mechanics to special relativity and then to general relativity are explored in detail as well, helping readers to gain a more profound and nuanced understanding of the theory as a whole. After reviewing the fundamentals of differential geometry and classical mechanics, the text introduces special relativity, first using the physical approach proposed by Einstein and then via Minkowski’s mathematical model. The authors then address the relativistic thermodynamics of continua and electromagnetic fields in matter – topics which are normally covered only very briefly in other treatments – in the next two chapters. The text then turns to a discussion of general relativity by means of the authors’ unique critical approach, underlining the difficulty of recognizing the physical meaning of some statements, such as the physical meaning of coordinates and the derivation of physical quantities from those of space-time. Chapters in this section cover the model of space-time proposed by Schwarzschild; black holes; the Friedman equations and the different cosmological models they describe; and the Fermi-Walker derivative. Well-suited for graduate students in physics and mathematics who have a strong foundation in real analysis, classical mechanics, and general physics, this textbook is appropriate for a variety of graduate-level courses that cover topics in relativity. Additionally, it will interest physicists and other researchers who wish to further study the subtleties of these theories and understand the contemporary scholarly discussions surrounding them.

Author : Hartmut Pilkuhn
Publisher : Springer Science & Business Media
ISBN 13 : 366205275X
Total Pages : 244 pages
Book Rating : 4.54/5 ( download)

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Download or read book Relativistic Quantum Mechanics written by Hartmut Pilkuhn and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, quantum mechanics is developed from the outset on a relativistic basis, using the superposition principle, Lorentz invariance and gauge invariance. Nonrelativistic quantum mechanics appears as a special case, and classical relativistic mechanics as another one. These special cases are important for giving plausible names to operators, for example "orbital angular momentum", "spin" or "magnetic moment". A subject which is treated for the first time in this book is the theory of binaries in terms of differential equations which have the mathematical structure of the corresponding one-body equations (Klein--Gordon for two spin- less particles, Dirac for two spinor particles).

Author : Walter Thirring
Publisher : Springer Science & Business Media
ISBN 13 : 9780387406152
Total Pages : 580 pages
Book Rating : 4.58/5 ( download)

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Download or read book Classical Mathematical Physics written by Walter Thirring and published by Springer Science & Business Media. This book was released on 2003-10-17 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume combines the enlarged and corrected editions of both volumes on classical physics of Thirring's famous course in mathematical physics. With numerous examples and remarks accompanying the text, it is suitable as a textbook for students in physics, mathematics, and applied mathematics. The treatment of classical dynamical systems uses analysis on manifolds to provide the mathematical setting for discussions of Hamiltonian systems, canonical transformations, constants of motion, and pertubation theory. Problems discussed in considerable detail include: nonrelativistic motion of particles and systems, relativistic motion in electromagnetic and gravitational fields, and the structure of black holes. The treatment of classical fields uses the language of differenial geometry throughout, treating both Maxwell's and Einstein's equations in a compact and clear fashion. The book includes discussions of the electromagnetic field due to known charge distributions and in the presence of conductors as well as a new section on gauge theories. It discusses the solutions of the Einstein equations for maximally symmetric spaces and spaces with maximally symmetric submanifolds; it concludes by applying these results to the life and death of stars.

Author : F. Strocchi
Publisher : World Scientific
ISBN 13 : 9812835229
Total Pages : 193 pages
Book Rating : 4.22/5 ( download)

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Download or read book An Introduction to the Mathematical Structure of Quantum Mechanics written by F. Strocchi and published by World Scientific. This book was released on 2008 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arising out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students, this book formulates the mathematical structure of QM in terms of the C*-algebra of observables, which is argued on the basis of the operational definition of measurements and the duality between states and observables.

Author : Andreas Knauf
Publisher : Springer
ISBN 13 : 3662557746
Total Pages : 683 pages
Book Rating : 4.47/5 ( download)

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Download or read book Mathematical Physics: Classical Mechanics written by Andreas Knauf and published by Springer. This book was released on 2018-02-24 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior. This book presents the KAM (Kolmogorov-Arnold-Moser) theory and asymptotic completeness in classical scattering. Including a wealth of fascinating examples in physics, it offers not only an excellent selection of basic topics, but also an introduction to a number of current areas of research in the field of classical mechanics. Thanks to the didactic structure and concise appendices, the presentation is self-contained and requires only knowledge of the basic courses in mathematics. The book addresses the needs of graduate and senior undergraduate students in mathematics and physics, and of researchers interested in approaching classical mechanics from a modern point of view.

Author : Walter Thirring
Publisher : Springer
ISBN 13 : 3662398923
Total Pages : 271 pages
Book Rating : 4.20/5 ( download)

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Download or read book Classical Dynamical Systems written by Walter Thirring and published by Springer. This book was released on 2013-12-01 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Michael Spivak
Publisher :
ISBN 13 : 9780914098324
Total Pages : 733 pages
Book Rating : 4.22/5 ( download)

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Download or read book Physics for Mathematicians written by Michael Spivak and published by . This book was released on 2010 with total page 733 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Somnath Datta
Publisher : World Scientific
ISBN 13 : 9811228132
Total Pages : 384 pages
Book Rating : 4.31/5 ( download)

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Download or read book Special Relativity, Tensors, And Energy Tensor: With Worked Problems written by Somnath Datta and published by World Scientific. This book was released on 2021-03-02 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes the reader from the preliminary ideas of the Special Theory of Relativity (STR) to the doorsteps of the General Theory of Relativity (GTR).The first part explains the main concepts in a layman's language, including STR, the Lorentz transformation, relativistic mechanics. Thereafter the concept of tensors is built up in detail, especially Maxwell's stress tensor with illustrative examples, culminating in the energy-momentum conservation in electromagnetic fields. Mathematical structure of Minkowski's space-time is constructed and explained graphically. The equation of motion is formulated and then illustrated by the example of relativistic rocket. The principle of covariance is explained with the covariant equations of classical electrodynamics. Finally, the book constructs the energy tensor which constitutes the source term in Einstein's field equation, which clears the passage to the GTR.In the book, the concepts of tensors are developed carefully and a large number of numerical examples taken from atomic and nuclear physics. The graphs of important equations are included. This is suitable for studies in classical electrodynamics, modern physics, and relativity.

Author : E C G Sudarshan
Publisher : World Scientific Publishing Company
ISBN 13 : 9814713899
Total Pages : 612 pages
Book Rating : 4.94/5 ( download)

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Download or read book Classical Dynamics written by E C G Sudarshan and published by World Scientific Publishing Company. This book was released on 2015-10-08 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical dynamics is traditionally treated as an early stage in the development of physics, a stage that has long been superseded by more ambitious theories. Here, in this book, classical dynamics is treated as a subject on its own as well as a research frontier. Incorporating insights gained over the past several decades, the essential principles of classical dynamics are presented, while demonstrating that a number of key results originally considered only in the context of quantum theory and particle physics, have their foundations in classical dynamics. Graduate students in physics and practicing physicists will welcome the present approach to classical dynamics that encompasses systems of particles, free and interacting fields, and coupled systems. Lie groups and Lie algebras are incorporated at a basic level and are used in describing space-time symmetry groups. There is an extensive discussion on constrained systems, Dirac brackets and their geometrical interpretation. The Lie-algebraic description of dynamical systems is discussed in detail, and Poisson brackets are developed as a realization of Lie brackets. Other topics include treatments of classical spin, elementary relativistic systems in the classical context, irreducible realizations of the Galileo and Poincaré groups, and hydrodynamics as a Galilean field theory. Students will also find that this approach that deals with problems of manifest covariance, the no-interaction theorem in Hamiltonian mechanics and the structure of action-at-a-distance theories provides all the essential preparatory groundwork for a passage to quantum field theory. This reprinting of the original text published in 1974 is a testimony to the vitality of the contents that has remained relevant over nearly half a century.