Matematisk fysik

This helpful and pedagogical book offers problems and solutions in quantum mechanics from areas of current research, rarely addressed in introductory courses or textbooks. It is based on the authors' own experience of teaching undergraduate and graduate courses in quantum mechanics, and adapts problems from contemporary research publications to be accessible to students. Each section introduces key quantum mechanical concepts, which are followed by exercises that grow progressively more challenging throughout the chapter. The step-by-step solutions provide detailed mathematical derivations, and explore their application to wider research topics. This is an indispensable resource for undergraduate and graduate students alike, expanding the range of topics usually covered in the classroom, as well as for instructors and early-career researchers in quantum mechanics, quantum computation and communication, and quantum information.

Many nonlinear systems around us can generate a very complex and counter-intuitive dynamics that contrasts with their simplicity, but their understanding requires concepts that are outside the basic training of most science students. This textbook, which is the fruit of graduate courses that the authors have taught at their respective universities, provides a richly illustrated introduction to nonlinear dynamical systems and chaos and a solid foundation for this fascinating subject. It will satisfy those who want discover this field, including at the undergraduate level, but also those who need a compact and consistent overview, gathering the concepts essential to nonlinear scientists.The first and second chapters describe the essential concepts needed to describe nonlinear dynamical systems as well as their stability. The third chapter introduces the concept of bifurcation, where the qualitative dynamical behavior of a system changes. The fourth chapter deals with oscillations, from their birth to their destabilization, and how they respond to external driving. The fifth and sixth chapters discuss complex behaviors that only occur in state spaces of dimension three and higher: quasi-periodicity and chaos, from their general properties to quantitative methods of characterization. All chapters are supplemented by exercises ranging from direct applications of the notions introduced in the corresponding chapter to elaborate problems involving concepts from different chapters, as well as numerical explorations.

This book introduces the reader to the study of Hamiltonian systems, focusing on the stability of autonomous and periodic systems and expanding to topics that are usually not covered by the canonical literature in the field. It emerged from lectures and seminars given at the Federal University of Pernambuco, Brazil, known as one of the leading research centers in the theory of Hamiltonian dynamics.This book starts with a brief review of some results of linear algebra and advanced calculus, followed by the basic theory of Hamiltonian systems. The study of normal forms of Hamiltonian systems is covered by Ch.3, while Chapters 4 and 5 treat the normalization of Hamiltonian matrices. Stability in non-linear and linear systems are topics in Chapters 6 and 7. This work finishes with a study of parametric resonance in Ch. 8. All the background needed is presented, from the Hamiltonian formulation of the laws of motion to the application of the Krein-Gelfand-Lidskii theory of stronglystable systems.With a clear, self-contained exposition, this work is a valuable help to advanced undergraduate and graduate students, and to mathematicians and physicists doing research on this topic.

This book offers supporting material for the comprehensive textbook Mathematical Physics¿A Modern Introduction to Its Foundations authored by Sadri Hassani. The book covers mathematical preliminaries and all of Part I in Hassani¿s textbook. The subjects covered here include the key topics necessary for physicists to form a solid mathematical foundation: vectors and linear maps, algebras, operators, matrices, and spectral decomposition. In particular, the vector space concept is a central unifying theme in later chapters of Hassani¿s textbook. Detailed solutions are provided to one third of the end-of-chapter exercises in the first six chapters of his text.The present volume helps upper-undergraduate and early postgraduate physics students deepen their understanding of the mathematics that they encounter in physics, learn physics more efficiently, and use mathematics with more confidence and creativity. The content is thus presented rigorously but remains accessible tophysics students.New exercises are also proposed, some with solutions, some without, so that the total number of unsolved exercises remains unchanged. They are chosen to help explain difficult concepts, amplify key points in Hassani's textbook, or make further connections with applications in physics. Taken together with Hassani's work, the two form a self-contained set and the solutions make detailed reference to Hassani's text. The solutions also refer to other mathematics and physics textbooks, providing entry points to further literature that finds a useful place in the physicist's personal library.

"This text provides a unique overview of the Maurer-Cartan methods in algebra, geometry, topology, and mathematical physics, offering a new conceptual treatment of the twisting procedure. It includes many motivating examples to render the theory accessible to graduate students, as well as a survey of recent applications"--

This book is a collection of invited contributions presented at the 8th edition of the International Workshop on Theory, Phenomenology and Experiments in Flavour Physics, held on the Island of Capri, Italy, on 11¿13 June 2022. It is a joint workshop between experimentalists and theoreticians aiming at debating recent results and hot topics in flavour physics, in an interdisciplinary effort. Flavour, electroweak physics and neutrino physics are all foremost in the assessment of results within the standard model and search for physics beyond. Anomalies in flavour physics are hints on new physics, while with neutrino masses and oscillations the new physics has already started. Contributions deal mainly with the flavour anomalies, the flavour problem from leptons to quarks and back, including continuous versus discrete symmetries, and the connections between the Higgs sector and neutrinos, embracing see-saw models and Higgs potential analyses. Focus is on neutrinos, at highand low scales, including LHC searches and CLVF, leptogenesis, connections with dark sectors and NP mediators, non-standard neutrino interactions and the problem of the nature of massive neutrinos.

This volume collects papers based on lectures given at the XXXIX Workshop on Geometric Methods in Physics, held in Biäystok, Poland in June 2022. These chapters provide readers an overview of cutting-edge research in geometry, analysis, and a wide variety of other areas. Specific topics include:Classical and quantum field theoriesInfinite-dimensional groupsIntegrable systemsLie groupoids and Lie algebroidsRepresentation theoryGeometric Methods in Physics XXXIX will be a valuable resource for mathematicians and physicists interested in recent developments at the intersection of these areas.

"Provides a broad and accessible introduction to quantum field theory and the Standard Model of particle physics, adopting a distinctive pedagogical approach with clear intuitive explanations to complement the mathematical exposition. Includes topics of current research both within and beyond the Standard Model"--

Wie lange liefert die Sonne genug Energie für unsere wachsende Bevölkerung?Reichen unsere Dächer aus, um genügend Solarstrom zu erzeugen?Stellen Pflanzen und Algen genug Nahrung und Sauerstoff für alle Lebewesen bereit?Millionen Menschen hungern. Strom ist für Milliarden Menschen ein Traum oder zumindest ein Luxusgut. Dieses Buch diskutiert mit Hilfe verständlich dargestellter Physik, wie weit es zu wenig Ressourcen gibt und wie weit es schlicht ein Problem der Verteilung ist.Das Buch ist gleichermaßen geeignet für Interessierte wie für Personen mit physikalischer Ausbildung. Zahlreiche Vergleiche und Erklärungen zeichnen ein anschauliches Bild, welches durch viele Abschätzungen und physikalische Details ergänzt wird.

Die beiden Bände von Quantenmechanik zu Fuß führen Schritt für Schritt in die Grundlagen der nichtrelativistischen Quantenmechanik ein.Dieser erste Band konzentriert sich hauptsächlich auf die wesentlichen Prinzipien, während Anwendungen und Erweiterungen des Formalismus in Band 2 zu finden sind.Um die Grundideen der Quantenmechanik und ihre mathematische Formulierung schnell und anschaulich darzustellen, wird in den ersten Kapiteln systematisch zwischen analytischer und algebraischer Darstellung gewechselt. Auf diese Weise können neben dem traditionellen Lehrstoff frühzeitig auch aktuelle Themen detailliert besprochen werden, wie z.B. Neutrino-Oszillationen und Quantenkryptographie. Ausgearbeitete Beispiele erleichtern den Zugang. Die erforderlichen mathematischen Werkzeuge werden dabei nach Bedarf eingeführt. Ein weiterer Schwerpunkt ist die Darstellung und Diskussion des Messproblems und anderer grundlegender konzeptueller Fragen. Ein Kapitel über die Postulate der Quantenmechanik schließt diesen ersten Band ab.Im Anhang findet sich eine kompakte Zusammenfassung der wichtigsten mathematischen Hilfsmittel, sodass auf ergänzende Literatur verzichten werden kann. Außerdem werden dort weiterführende Themen wie der Quanten-Zeno-Effekt und Time-delay-Experimente behandelt. Über 250 Übungsaufgaben mit ausführlichen Lösungen helfen dabei, das Verständnis für die behandelten Themen zu vertiefen.Die vorliegende überarbeitete und aktualisierte zweite Auflage ist um eine Einführung in einige Ideen und Probleme der relativistischen Quantenmechanik erweitert. In diesem ersten Band werden die Klein-Gordon- und die Dirac-Gleichung behandelt. Für die Relativistik benötigte Grundlagen anderer Gebiete werden in kompakter Form bereit gestellt (spezielle Relativitätstheorie, klassische Feldtheorie und Elektrodynamik).Quantenmechanik zu Fuß richtet sich an alle Studierenden der Physik und andere, die eine angemessen einfache, frische und moderne Einführung in die Quantenmechanik suchen. Das Buch eignet sich auch sehr gut zum Selbststudium.

Die beiden Bände von Quantenmechanik zu Fuß führen Schritt für Schritt in die Grundlagen der nichtrelativistischen Quantenmechanik ein.Während sich der erste Band mit den wesentlichen Prinzipien befasst, werden in diesem zweiten Band Anwendungen und Erweiterungen auf komplexere Probleme erörtert.Neben Gebieten, die zum traditionellen Stoff der Quantenmechanik gehören wie z.B. Symmetrien, Streutheorie oder Vielteilchenprobleme, werden auch aktuelle Themen ausführlich behandelt, etwa Verschränkung, Bellsche Ungleichung, Dekohärenz, Quantencomputer und andere Aspekte der Quanteninformation. Ausgearbeitete Beispiele erleichtern den Zugang. Die Realismusdebatte und andere konzeptuelle Fragen der Quantenmechanik werden ausführlich besprochen. Ein Kapitel über die Interpretationen der Quantenmechanik schließt diesen zweiten Band ab.Im Anhang wird das erforderliche mathematische Handwerkszeug kompakt zusammengestellt. Außerdem werden dort weiterführendeThemen wie der Lenz-Vektor, das Hardy-Experiment und der Shor-Algorithmus detailliert dargestellt. Über 150 Übungsaufgaben mit ausführlichen Lösungen helfen dabei, das Verständnis für die behandelten Themen zu vertiefen. Die vorliegende überarbeitete und aktualisierte zweite Auflage ist um eine Einführung in einige Ideen und Probleme der relativistischen Quantenmechanik erweitert. In diesem zweiten Band wird ein Überblick über die Quantenfeldtheorie gegeben und grundlegende Konzepte der Quantenelektrodynamik eingehend behandelt.Quantenmechanik zu Fuß richtet sich an alle Studierenden der Physik und andere, die eine angemessen einfache, frische und moderne Einführung in die Quantenmechanik suchen. Das Buch eignet sich auch sehr gut zum Selbststudium.

This book gives a comprehensive introduction to those parts of the theory of elliptic integrals and elliptic functions which provide illuminating examples in complex analysis, but which are not often covered in regular university courses. These examples form prototypes of major ideas in modern mathematics and were a driving force of the subject in the eighteenth and nineteenth centuries. In addition to giving an account of the main topics of the theory, the book also describes many applications, both in mathematics and in physics. For the reader¿s convenience, all necessary preliminaries on basic notions such as Riemann surfaces are explained to a level sufficient to read the book.For each notion a clear motivation is given for its study, answering the question ¿Why do we consider such objects?¿, and the theory is developed in a natural way that mirrors its historical development (e.g., ¿If there is such and such an object, then you would surely expect this one¿). This feature sets this text apart from other books on the same theme, which are usually presented in a different order. Throughout, the concepts are augmented and clarified by numerous illustrations. Suitable for undergraduate and graduate students of mathematics, the book will also be of interest to researchers who are not familiar with elliptic functions and integrals, as well as math enthusiasts.

This book provides a mathematical and numerical analysis of many problems which lead to paradoxes in contemporary cosmology, in particular, the existence of dark matter and dark energy. It is shown that these hypothetical quantities arise from excessive extrapolations of simple mathematical models to the whole physical universe. Written in a completely different style to most books on General Relativity and cosmology, the important results take the form of mathematical theorems with precise assumptions and statements. All theorems are followed by a corresponding proof, or an exact reference to the proof.Some nonstandard topics are also covered, including violation of the causality principle in Newtonian mechanics, a critical mathematical and numerical analysis of Mercury's perihelion shift, inapplicability of Einstein's equations to the classical two-body problem due to computational complexity, non-uniqueness of the notion of universe, the topology of the universe, various descriptions of a hypersphere, regular tessellations of hyperbolic spaces, local Hubble expansion of the universe, neglected gravitational redshift in the detection of gravitational waves, and the possible distribution of mass inside a black hole. The book also dispels some myths appearing in the theory of relativity and in contemporary cosmology. For example, although the hidden assumption that Einstein's equations provide a good description of the evolution of the whole universe is considered to be obvious, it is just a null hypothesis which has not been verified by any experiment, and has only been postulated by excessive extrapolations of many orders of magnitude.

The NUMISHEET conference series is the most significant international conference on the area of the numerical simulation of sheet metal forming processes. It gathers the most prominent experts in numerical methods in sheet forming processes and is an outstanding forum for the exchange of ideas and for the discussion of technologies related to sheet metal forming processes. Topics covered in this volume include but are not limited to the following: Materials Modeling and Experimental Testing MethodsFriction and ContactFormability, Necking, and FractureInstabilities and Surface DefectsFracture and DamageNumerical MethodsSpringbackIncremental Sheet FormingRoll FormingInnovative Forming MethodsProduct and Process Design and Optimization

This book highlights an analytical solution for the dynamics of axially rotating objects. It also presents the theory of gyroscopic effects, explaining their physics and using mathematical models of Euler's form for the motion of movable spinning objects to demonstrate these effects. The major themes and approaches are represented by the spinning disc and the action of the system of interrelated inertial torques generated by the centrifugal and Coriolis forces, as well as the change in the angular momentum. The interrelation of inertial torques is based on the dependency of the angular velocities of the motions of the spinning objects around axes by the principle of mechanical energy conservation. These kinetically interrelated torques constitute the fundamental principles of the mechanical gyroscope theory that can be used for any rotating objects of different designs, like rings, cones, spheres, paraboloids, propellers, etc. Lastly, the mathematical models for the gyroscopic effects are validated by practical tests.  The 2nd edition became necessary due to new development and corrections of mathematical expressions: It contains new chapters about the Tippe top inversion and inversion of the spinning object in an orbital flight and the boomerang aerodynamics.

This monograph provides a complete and up-to-date examination of rigid body dynamics using a Lagrangian approach. All known integrable cases, which were previously scattered throughout the literature, are collected here for convenient reference. Also contained are particular solutions to diverse problems treated within rigid body dynamics.The first seven chapters introduce the elementary dynamics of the rigid body and its main problems. A full historical account of the discovery and development of each of the integrable cases is included as well. Instructors will find this portion of the book well-suited for an undergraduate course, having been formulated by the author in the classroom over many years.The second part includes more advanced topics and some of the author's original research, highlighting several unique methods he developed that have led to significant results. Some of the specific topics covered include the twelve known solutions of the equations of motion in the classical problem, which has not previously appeared in English before; a collection of completely new integrable cases; and the motion of a rigid body around a fixed point under the action of an asymmetric combination of potential and gyroscopic forces.Rigid Body Dynamics will appeal to researchers in the area as well as those studying dynamical and integrable systems theory.

Von der Physik bis zur Informationstheorie und Kosmologie, von der Struktur tierischer Gesellschaften bis zur linguistischen Analyse der menschlichen Schrift zeigen Systeme, die aus vielen interagierenden Bestandteilen bestehen, oft ein kollektives Verhalten, das sich nicht aus der Interaktion der einzelnen Bestandteile vorhersagen lässt. In Mehr als die Summe der Teile befasst sich Helmut Satz mit verschiedenen Formen dieses komplexen Verhaltens, die erst in den letzten Jahrzehnten gründlich untersucht worden sind. Obwohl diese Studien ihren Ursprung in der Physik haben, erweist sich das Verhalten als universell und reicht von der Struktur des frühen Universums über die Bildung von Vogelschwärmen bis hin zur Häufigkeit von Wörtern in literarischen Texten. Die Komplexität wird somit zu einem immer wichtigeren interdisziplinären Bereich für die künftige wissenschaftliche Forschung.Auf konzeptionelle und nicht-technische Weise erschließt Satz dieses spannende Gebiet für eine allgemeine Leserschaft und für Studierende aller naturwissenschaftlichen Fächer.

Non-Abelian gauge theories, such as quantum chromodynamics (QCD) or electroweak theory, are best studied with the aid of Green's functions that are gauge-invariant off-shell, but unlike for the photon in quantum electrodynamics, conventional graphical constructions fail. The pinch technique provides a systematic framework for constructing such Green's functions, and has many useful applications. Beginning with elementary one-loop examples, this book goes on to extend the method to all orders, showing that the pinch technique is equivalent to calculations in the background field Feynman gauge. The Schwinger-Dyson equations are derived within the pinch technique framework, and are used to show how a dynamical gluon mass arises in QCD. Finally the volume turns to its many applications. This book is ideal for elementary particle theorists and graduate students. This 2011 title has been reissued as an Open Access publication on Cambridge Core.

Originally published in 1977, this book presents an extended introduction to the theory of hadrons, the elementary particles which occur in the atomic nucleus. The main emphasis is on the theory of the complex angular momentum plane 'Regge theory', which has grown from Regge's demonstration in 1959 that it is useful to regard angular momentum as a complex variable when discussing solutions of the Schrodinger equation for non-relativistic potential scattering. This theory helps to classify the many different particles which have been discovered in recent years, to explain the forces between these particles and to predict the results of high-energy scattering experiments. Regge theory thus serves as a unifying concept drawing together many different features of high-energy physics. This monograph is intended primarily for research students just beginning to concern themselves with particle physics, but more experienced workers will also find much to interest them in this detailed survey of the basic ideas and results of Regge theory.

A clear and original introductory 2000 text on the physics of heavy quarks, written by two world leading experts.

This book develops the basic formalism and theoretical techniques for studying relativistic quantum field theory at high temperature and density. Specific physical theories treated include QED, QCD, electroweak theory, and effective nuclear field theories of hadronic and nuclear matter. Topics covered include: functional integral representation of the partition function, diagrammatic expansions, linear response theory, screening and plasma oscillations, spontaneous symmetry breaking, Goldstone theorem, resummation and hard thermal loops, lattice gauge theory, phase transitions, nucleation theory, quark-gluon plasma, and color superconductivity. Applications to astrophysics and cosmology cover white dwarf and neutron stars, neutrino emissivity, baryon number violation in the early universe, and cosmological phase transitions. Applications to relativistic nucleus-nucleus collisions are also included. The book is written for theorists in elementary particle physics, nuclear physics, astrophysics, and cosmology. Released initially in 2006, this title has been reissued as an Open Access publication on Cambridge Core.