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.
One could make the claim that all branches of physics are basically generalizations of classical mechanics. It is also often the first course which is taught to physics students. The approach of this book is to construct an intermediate discipline between general courses of physics and analytical mechanics, using more sophisticated mathematical tools. The aim of this book is to prepare a self-consistent and compact text that is very useful for teachers as well as for independent study.
Der Goldstein gehört zu den Standardwerken für die Vorlesung in Klassischer Mechanik, die Pflichtvorlesung und Teil des Theorie-Lehrplans jedes Physik-Studienganges ist. Für diese aktuelle Ausgabe haben Charles Poole und John Safko die Texte überarbeitet und neueste Themen, Anwendungen und Notationen eingearbeitet und sind damit auf moderne Trends in der Theoretischen Mechanik eingegangen. Neue numerische Übungen verhelfen den Studenten zur Fähigkeit, Computeranwendungen für die Lösung von Physikproblemen zu benutzen. Mathematische Techniken werden detailliert eingeführt, so daß der Text auch für Studenten ohne den entsprechenden Hintergrund der Theoretischen Mechanik verständlich ist.
Der Grundkurs Theoretische Physik deckt in sieben Bänden alle für Diplom- und Bachelor/Master-Studiengänge maßgeblichen Gebiete ab. Jeder Band vermittelt das im jeweiligen Semester nötige theoretisch-physikalische Rüstzeug. Übungsaufgaben mit ausführlichen Lösungen dienen der Vertiefung des Stoffs. Band 1 behandelt die klassische Mechanik. Vorausgesetzt wird nur die übliche Schulmathematik, andere mathematische Hilfsmittel werden zu Beginn ausführlich erläutert. Die zweifarbig gestaltete Neuauflage wurde grundlegend überarbeitet und ergänzt.
Differentialgeometrie und Topologie sind wichtige Werkzeuge für die Theoretische Physik. Insbesondere finden sie Anwendung in den Gebieten der Astrophysik, der Teilchen- und Festkörperphysik. Das vorliegende beliebte Buch, das nun erstmals ins Deutsche übersetzt wurde, ist eine ideale Einführung für Masterstudenten und Forscher im Bereich der theoretischen und mathematischen Physik. - Im ersten Kapitel bietet das Buch einen Überblick über die Pfadintegralmethode und Eichtheorien. - Kapitel 2 beschäftigt sich mit den mathematischen Grundlagen von Abbildungen, Vektorräumen und der Topologie. - Die folgenden Kapitel beschäftigen sich mit fortgeschritteneren Konzepten der Geometrie und Topologie und diskutieren auch deren Anwendungen im Bereich der Flüssigkristalle, bei suprafluidem Helium, in der ART und der bosonischen Stringtheorie. - Daran anschließend findet eine Zusammenführung von Geometrie und Topologie statt: es geht um Faserbündel, characteristische Klassen und Indextheoreme (u.a. in Anwendung auf die supersymmetrische Quantenmechanik). - Die letzten beiden Kapitel widmen sich der spannendsten Anwendung von Geometrie und Topologie in der modernen Physik, nämlich den Eichfeldtheorien und der Analyse der Polakov'schen bosonischen Stringtheorie aus einer gemetrischen Perspektive. Mikio Nakahara studierte an der Universität Kyoto und am King’s in London Physik sowie klassische und Quantengravitationstheorie. Heute ist er Physikprofessor an der Kinki-Universität in Osaka (Japan), wo er u. a. über topologische Quantencomputer forscht. Diese Buch entstand aus einer Vorlesung, die er während Forschungsaufenthalten an der University of Sussex und an der Helsinki University of Sussex gehalten hat.
Today many important directions of research are being pursued more or less independently of each other. These are, for instance, strings and mem branes, induced gravity, embedding of spacetime into a higher dimensional space, the brane world scenario, the quantum theory in curved spaces, Fock Schwinger proper time formalism, parametrized relativistic quantum the ory, quantum gravity, wormholes and the problem of “time machines”, spin and supersymmetry, geometric calculus based on Clifford algebra, various interpretations of quantum mechanics including the Everett interpretation, and the recent important approach known as “decoherence”. A big problem, as I see it, is that various people thoroughly investigate their narrow field without being aware of certain very close relations to other fields of research. What we need now is not only to see the trees but also the forest. In the present book I intend to do just that: to carry out a first approximation to a synthesis of the related fundamental theories of physics. I sincerely hope that such a book will be useful to physicists. From a certain viewpoint the book could be considered as a course in the oretical physics in which the foundations of all those relevant fundamental theories and concepts are attempted to be thoroughly reviewed. Unsolved problems and paradoxes are pointed out. I show that most of those ap proaches have a common basis in the theory of unconstrained membranes. The very interesting and important concept of membrane space, the tensor calculus in and functional transformations in are discussed.
Written by two researchers in the field, this book is a reference to explain the principles and fundamentals in a self–contained, complete and consistent way. Much attention is paid to the didactical value, with the chapters interconnected and based on each other. From the contents: ∗ Fundamentals ∗ Relativistic Theory of a Free Electron: Dirac´s Equation ∗ Dirac Theory of a Single Electron in a Central Potential ∗ Many–Electron Theory I: Quantum Electrodynamics ∗ Many–Electron Theory II: Dirac–Hartree–Fock Theory ∗ Elimination of the Small Component ∗ Unitary Transformation Schemes ∗ Relativistic Density Functional Theory ∗ Physical Observables and Molecular Properties ∗ Interpretive Approach to Relativistic Quantum Chemistry From beginning to end, the authors deduce all the concepts and rules, such that readers are able to understand the fundamentals and principles behind the theory. Essential reading for theoretical chemists and physicists.
in this work, we must therefore assume several abstract concepts that hardly need defending at this point in the history of mechanics. Most notably, these include the concept of the point particle and the concept of the inertial observer. The study of the relativistic particle system is undertaken here by means of a particular classical theory, which also exists on the quantum level, and which is especially suited to the many-body system in flat spacetime. In its fundamental postulates, the theory may be consid ered to be primarily the work of E.C.G. Stiickelberg in the 1940's, and of L.P. Horwitz and C. Piron in the 1970's, who may be said to have provided the generalization of Stiickelberg's theory to the many-body system. The references for these works may be found in Chapter 1. The theory itself may be legitimately called off-shell Hamiltonian dynamics, parameterized relativistic mechanics, or even classical event dynamics. The most important feature of the theory is probably the use of an invariant world time parameter, usually denoted T, which provides an evolution time for the system in such as way as to allow manifest co variance within a Hamiltonian formalism. In general, this parameter is neither a Lorentz-frame time, nor the proper time of the particles in the system.
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.
Originally written in 1964, this famous text is a study of the classical theory of charged particles. Many applications treat electrons as point particles. At the same time, there is a widespread belief that the theory of point particles is beset with various difficulties such as an infinite electrostatic self-energy, a rather doubtful equation of motion which admits physically meaningless solutions, violation of causality and others. The classical theory of charged particles has been largely ignored and has been left in an incomplete state since the discovery of quantum mechanics. Despite the great efforts of men such as Lorentz, Abraham, Poincar‚, and Dirac, it is usually regarded as a ?lost cause?. But thanks to progress made just a few years ago, the author is able to resolve the various problems and to complete this unfinished theory successfully.
Formalism of classical mechanics underlies a number of powerful mathematical methods that are widely used in theoretical and mathematical physics. This book considers the basics facts of Lagrangian and Hamiltonian mechanics, as well as related topics, such as canonical transformations, integral invariants, potential motion in geometric setting, symmetries, the Noether theorem and systems with constraints. While in some cases the formalism is developed beyond the traditional level adopted in the standard textbooks on classical mechanics, only elementary mathematical methods are used in the exposition of the material. The mathematical constructions involved are explicitly described and explained, so the book can be a good starting point for the undergraduate student new to this field. At the same time and where possible, intuitive motivations are replaced by explicit proofs and direct computations, preserving the level of rigor that makes the book useful for the graduate students intending to work in one of the branches of the vast field of theoretical physics. To illustrate how classical-mechanics formalism works in other branches of theoretical physics, examples related to electrodynamics, as well as to relativistic and quantum mechanics, are included.
Comprehensive graduate-level text by a distinguished theoretical physicist reveals the classical underpinnings of modern quantum field theory. Topics include space-time, Lorentz transformations, conservation laws, equations of motion, Green’s functions, and more. 1964 edition.
Das Buch bietet eine Einführung in die zum Studium der Theoretischen Physik notwendigen mathematischen Grundlagen. Der erste Teil des Buches beschäftigt sich mit der Theorie der Distributionen und vermittelt daneben einige Grundbegriffe der linearen Funktionalanalysis. Der zweite Teil baut darauf auf und gibt eine auf das Wesentliche beschränkte Einführung in die Theorie der linearen Operatoren in Hilbert-Räumen. Beide Teile werden von je einer Übersicht begleitet, die die zentralen Ideen und Begriffe knapp erläutert und den Inhalt kurz beschreibt. In den Anhängen werden einige grundlegende Konstruktionen und Konzepte der Funktionalanalysis dargestellt und wichtige Konsequenzen entwickelt.

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