The Mathematical Structure Of Classical And Relativistic Physics

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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 : 4.4/5 (614 download)

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Book Synopsis The Mathematical Structure of Classical and Relativistic Physics by : Enzo Tonti

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.

The Physical and Mathematical Foundations of the Theory of Relativity

Author : Antonio Romano
Publisher : Springer Nature
ISBN 13 : 3030272370
Total Pages : 496 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis The Physical and Mathematical Foundations of the Theory of Relativity by : Antonio Romano

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.

Classical Mathematical Physics

Author : Walter Thirring
Publisher : Springer Science & Business Media
ISBN 13 : 9780387406152
Total Pages : 580 pages
Book Rating : 4.4/5 (61 download)

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Book Synopsis Classical Mathematical Physics by : Walter Thirring

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.

An Introduction to the Mathematical Structure of Quantum Mechanics

Author : F. Strocchi
Publisher : World Scientific
ISBN 13 : 9812835229
Total Pages : 193 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis An Introduction to the Mathematical Structure of Quantum Mechanics by : F. Strocchi

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.

Mathematical Physics: Classical Mechanics

Author : Andreas Knauf
Publisher : Springer
ISBN 13 : 3662557746
Total Pages : 683 pages
Book Rating : 4.6/5 (625 download)

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Book Synopsis Mathematical Physics: Classical Mechanics by : Andreas Knauf

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.

Relativistic Quantum Mechanics

Author : Hartmut Pilkuhn
Publisher : Springer Science & Business Media
ISBN 13 : 366205275X
Total Pages : 244 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Relativistic Quantum Mechanics by : Hartmut Pilkuhn

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).

Physics for Mathematicians

Author : Michael Spivak
Publisher :
ISBN 13 : 9780914098324
Total Pages : 733 pages
Book Rating : 4.0/5 (983 download)

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Book Synopsis Physics for Mathematicians by : Michael Spivak

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:

Classical Dynamics

Author : E C G Sudarshan
Publisher : World Scientific Publishing Company
ISBN 13 : 9814713899
Total Pages : 612 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis Classical Dynamics by : E C G Sudarshan

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.

Classical Mechanics

Author : Walter Greiner
Publisher : Springer Science & Business Media
ISBN 13 : 0387218513
Total Pages : 488 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Classical Mechanics by : Walter Greiner

Download or read book Classical Mechanics written by Walter Greiner and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for advanced undergraduates and beginning graduate students, this text is based on the highly successful course given by Walter Greiner at the University of Frankfurt, Germany. The two volumes on classical mechanics provide not only a complete survey of the topic but also an enormous number of worked examples and problems to show students clearly how to apply the abstract principles to realistic problems.

Classical Dynamical Systems

Author : Walter Thirring
Publisher : Springer
ISBN 13 : 3662398923
Total Pages : 271 pages
Book Rating : 4.6/5 (623 download)

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Book Synopsis Classical Dynamical Systems by : Walter Thirring

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:

Special Relativity, Tensors, And Energy Tensor: With Worked Problems

Author : Somnath Datta
Publisher : World Scientific
ISBN 13 : 9811228132
Total Pages : 384 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Special Relativity, Tensors, And Energy Tensor: With Worked Problems by : Somnath Datta

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.

The Mathematical Principles of Scale Relativity Physics

Author : Nicolae Mazilu
Publisher : CRC Press
ISBN 13 : 1000751023
Total Pages : 256 pages
Book Rating : 4.0/5 (7 download)

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Book Synopsis The Mathematical Principles of Scale Relativity Physics by : Nicolae Mazilu

Download or read book The Mathematical Principles of Scale Relativity Physics written by Nicolae Mazilu and published by CRC Press. This book was released on 2019-09-12 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematical Principles of Scale Relativity Physics: The Concept of Interpretation explores and builds upon the principles of Laurent Nottale’s scale relativity. The authors address a variety of problems encountered by researchers studying the dynamics of physical systems. It explores Madelung fluid from a wave mechanics point of view, showing that confinement and asymptotic freedom are the fundamental laws of modern natural philosophy. It then probes Nottale’s scale transition description, offering a sound mathematical principle based on continuous group theory. The book provides a comprehensive overview of the matter to the reader via a generalization of relativity, a theory of colors, and classical electrodynamics. Key Features: Develops the concept of scale relativity interpreted according to its initial definition enticed by the birth of wave and quantum mechanics Provides the fundamental equations necessary for interpretation of matter, describing the ensembles of free particles according to the concepts of confinement and asymptotic freedom Establishes a natural connection between the Newtonian forces and the Planck’s law from the point of view of space and time scale transition: both are expressions of invariance to scale transition The work will be of great interest to graduate students, doctoral candidates, and academic researchers working in mathematics and physics.

Fundamental Principles of Classical Mechanics

Author : Kai S Lam
Publisher : World Scientific Publishing Company
ISBN 13 : 9814551503
Total Pages : 592 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Fundamental Principles of Classical Mechanics by : Kai S Lam

Download or read book Fundamental Principles of Classical Mechanics written by Kai S Lam and published by World Scientific Publishing Company. This book was released on 2014-07-07 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written with the belief that classical mechanics, as a theoretical discipline, possesses an inherent beauty, depth, and richness that far transcends its immediate applications in mechanical systems. These properties are manifested, by and large, through the coherence and elegance of the mathematical structure underlying the discipline, and are eminently worthy of being communicated to physics students at the earliest stage possible. This volume is therefore addressed mainly to advanced undergraduate and beginning graduate physics students who are interested in the application of modern mathematical methods in classical mechanics, in particular, those derived from the fields of topology and differential geometry, and also to the occasional mathematics student who is interested in important physics applications of these areas of mathematics. Its main purpose is to offer an introductory and broad glimpse of the majestic edifice of the mathematical theory of classical dynamics, not only in the time-honored analytical tradition of Newton, Laplace, Lagrange, Hamilton, Jacobi, and Whittaker, but also the more topological/geometrical one established by Poincare, and enriched by Birkhoff, Lyapunov, Smale, Siegel, Kolmogorov, Arnold, and Moser (as well as many others).

Unification of Classical, Quantum, and Relativistic Mechanics and of the Four Forces

Author : J. X. Zheng-Johansson
Publisher : Nova Publishers
ISBN 13 : 9781594542602
Total Pages : 266 pages
Book Rating : 4.5/5 (426 download)

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Book Synopsis Unification of Classical, Quantum, and Relativistic Mechanics and of the Four Forces by : J. X. Zheng-Johansson

Download or read book Unification of Classical, Quantum, and Relativistic Mechanics and of the Four Forces written by J. X. Zheng-Johansson and published by Nova Publishers. This book was released on 2006 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book Drs J X Zheng-Johansson and Per-Ivar Johansson present a remarkable unification scheme. The scheme is based on an analysis of the overall experimental observations available up to today, and an observation of the unsolved problems maintained in contemporary theoretical physics, revisiting past controversies and putting them in context with contemporary physics. The unsolved problems were the agent stimulating the authors to invent a new bold unification scheme. Vacuum polarisation, with a vacuuon (a pair of strongly bound opposite-signed charges) as a free entity, gets you back to the days of the ether concept, abandoned by physics after the Michelson-Morley experiment by the end of the 19:th century. Starting from constructing the fundamental building blocks for the vacuum and material particles, the Newtonian-Maxwellian solutions the authors obtain yield insights into fundamental concepts such as vacuum, charge, and mass. For instance, can vacuum be described by a building block denoted vacuuon, with or without mass depending on pushed into motion or not? Can free charges be described as a mass-less entity? Can and how vacuum polarise? However, even if vacuum in the real Universe never polarises as proposed in this unification scheme, it may yet serve as another tool in the physics toolbox, a theoretical bridge between classical and modern physics. Physics and physical theory is a human invention, a mathematical description of the intrinsic properties of the Universe and its associated phenomena. Our understanding of the Universe is a reaction of our mind, of our way of understanding. Richard Feynman once noted about the Maxwell equations something that goes like: If a mathematical theory in physics cannot be proved by experiments it remains to be proved mathematically. Ultimately, it must be possible to test any new theory by experiments. If experimental tests are not possible we are left with a mere hypothesis based on equations. The unification scheme proposed by this work consists of a Proposition about the fundamental building blocks (ap- and n-vaculeon) and a series of Predictions from Newtonian-Maxwellian solutions based on that Proposition. The arriving at the Proposition and the Predictions, relating to classical, quantum and relativistic mechanics, is their context. The book is a challenge out of the ordinary, a challenge that deserves careful consideration.

Physical Applications of Homogeneous Balls

Author : Yaakov Friedman
Publisher : Springer Science & Business Media
ISBN 13 : 0817682082
Total Pages : 297 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Physical Applications of Homogeneous Balls by : Yaakov Friedman

Download or read book Physical Applications of Homogeneous Balls written by Yaakov Friedman and published by Springer Science & Business Media. This book was released on 2013-01-08 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Develops new tools to efficiently describe different branches of physics within one mathematical framework * Gives a clear geometric expression of the symmetry of physical laws * Useful for researchers and graduate students interested in the many physical applications of bounded symmetric domains * Will also benefit a wider audience of mathematicians, physicists, and graduate students working in relativity, geometry, and Lie theory

Relativity

Author : Roger B. Angel
Publisher : Elsevier
ISBN 13 : 1483139263
Total Pages : 272 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Relativity by : Roger B. Angel

Download or read book Relativity written by Roger B. Angel and published by Elsevier. This book was released on 2014-05-20 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Relativity: The Theory and its Philosophy provides a completely self-contained treatment of the philosophical foundations of the theory of relativity. It also surveys the most essential mathematical techniques and concepts that are indispensable to an understanding of the foundations of both the special and general theories of relativity. In short, the book includes a crash course in applied mathematics, ranging from elementary trigonometry to the classical tensor calculus. Comprised of 11 chapters, this book begins with an introduction to fundamental mathematical concepts such as sets, relations, and functions; N-tuples, vectors, and matrices; and vector algebra and calculus. The discussion then turns to the concept of relativity and elementary foundations of Newtonian mechanics, as well as the principle of special relativity and its philosophical interpretation by means of empiricism and rationalism. Subsequent chapters focus on the status of the doctrine of conventionalism in the theory of special relativity; the commensurability of classical and relativistic mechanics; mathematical foundations of special relativistic physics; and the classical or Newtonian theory of gravitation. The principle of general covariance and its relation to the principle of general relativity are also examined. The final chapter addresses the fundamental question as to the actual information concerning the structure of spacetime that is conveyed to us through the theory of general relativity. This monograph will be of interest to students, teachers, practitioners, and researchers in physics, mathematics, and philosophy.

An Introduction to the Relativistic Theory of Gravitation

Author : Petr Hajicek
Publisher : Springer
ISBN 13 : 9783540871170
Total Pages : 280 pages
Book Rating : 4.8/5 (711 download)

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Book Synopsis An Introduction to the Relativistic Theory of Gravitation by : Petr Hajicek

Download or read book An Introduction to the Relativistic Theory of Gravitation written by Petr Hajicek and published by Springer. This book was released on 2009-08-29 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contemporary theoretical physics consists, by and large, of two independent parts. The rst is the quantum theory describing the micro-world of elementary p- ticles, the second is the theory of gravity that concerns properties of macroscopic systems such as stars, galaxies, and the universe. The relativistic theory of gr- itation which is known as general relativity was created, at the beginning of the last century, by more or less a single man from pure idea combinations and bold guessing. The task was to “marry” the theory of gravity with the theory of special relativity. The rst attempts were aimed at considering the gravitational potential as a eld in Minkowski space–time. All those attempts failed; it took 10 years until Einstein nally solved the problem. The dif culty was that the old theory of gravity as well as the young theory of special relativity had to be modi ed. The next 50 years were dif cult for this theory because its experimental basis remained weak and its complicated mathematical structure was not well understood. However, in the subsequent period this theory ourished. Thanks to improvements in the te- nology and to the big progress in the methods of astronomical observations, the amount of observable facts to which general relativity is applicable was consid- ably enlarged. This is why general relativity is, today, one of the best experimentally tested theories while many competing theories could be disproved. Also the conc- tual and mathematical fundamentals are better understood now.