Matematisk fysik

This 2002 book introduces the quantum theory of gauge fields. Emphasis is placed on four non-perturbative methods: path integrals, lattice gauge theories, the 1/N expansion, and reduced matrix models, all of which have important contemporary applications. Written as a textbook, it assumes a knowledge of quantum mechanics and elements of perturbation theory, while many relevant concepts are pedagogically introduced at a basic level in the first half of the book. The second half comprehensively covers large-N Yang-Mills theory. The book uses an approach to gauge theories based on path-dependent phase factors known as the Wilson loops, and contains problems with detailed solutions to aid understanding. Suitable for advanced graduate courses in quantum field theory, the book will also be of interest to researchers in high energy theory and condensed matter physics as a survey of recent developments in gauge theory.

This book provides a coherent exposition of the techniques underlying these calculations.

Providing a new perspective on quantum field theory, this book gives a pedagogical and up-to-date exposition of non-perturbative methods in relativistic quantum field theory and introduces the reader to modern research work in theoretical physics. It describes in detail non-perturbative methods in quantum field theory, and explores two- dimensional and four- dimensional gauge dynamics using those methods. The book concludes with a summary emphasizing the interplay between two- and four- dimensional gauge theories. Aimed at graduate students and researchers, this book covers topics from two-dimensional conformal symmetry, affine Lie algebras, solitons, integrable models, bosonization, and 't Hooft model, to four-dimensional conformal invariance, integrability, large N expansion, Skyrme model, monopoles and instantons. Applications, first to simple field theories and gauge dynamics in two dimensions, and then to gauge theories in four dimensions and quantum chromodynamics (QCD) in particular, are thoroughly described.

This book was originally published in 2006. Moonshine forms a way of explaining the mysterious connection between the monster finite group and modular functions from classical number theory. The theory has evolved to describe the relationship between finite groups, modular forms and vertex operator algebras. Moonshine Beyond the Monster describes the general theory of Moonshine and its underlying concepts, emphasising the interconnections between mathematics and mathematical physics. Written in a clear and pedagogical style, this book is ideal for graduate students and researchers working in areas such as conformal field theory, string theory, algebra, number theory, geometry and functional analysis. Containing over a hundred exercises, it is also a suitable textbook for graduate courses on Moonshine and as supplementary reading for courses on conformal field theory and string theory.

The book provides readers with a snapshot of recent research and industrial trends in field of industrial acoustics and vibration. Each chapter, accepted after a rigorous peer-review process, reports on a selected, original piece of work presented and discussed at the Fourth International Conference on Acoustics and Vibration (ICAV2022), which was organized by the Tunisian Association of Industrial Acoustics and Vibration (ATAVI) and held in hybrid format on December 19¿21, 2022, in and from Sousse, Tunisia. The contributions cover advances in both theory and practice in a variety of subfields, such as structural and machine dynamics and vibrations, fault diagnosis and prognosis, nonlinear dynamics, and vibration control of mechatronic systems. Further topics include fluid¿structure interaction, computational vibro-acoustics, vibration field measurements, and dynamic behavior of materials. This book provides a valuable resource for both academics and professionals dealing with diverse issues in applied mechanics. By combining advanced theories with industrial issues, it is expected to facilitate communication and collaboration between different groups of researchers and technology users.

This book collects a selection of papers presented at ELECTRIMACS 2021, the 14th international conference of the IMACS TC1 Committee, held in Nancy, France, on 16th-19th May 2022. The conference papers deal with modelling, simulation, analysis, control, power management, design optimization, identification and diagnostics in electrical power engineering. The main application fields include electric machines and electromagnetic devices, power electronics, transportation systems, smart grids, renewable energy systems, energy storage like batteries and supercapacitors, fuel cells, and wireless power transfer. The contributions included in Volume 1 will be particularly focused on electrical engineering simulation aspects and innovative applications.

This book ¿offers step-by-step descriptions of various random systems and explores the world of computer simulations. In addition, this book offers a working introduction to those who want to learn how to create and run Monte Carlo simulations. Monte Carlo simulation has been a powerful computational tool for physics models, and when combined with the programming language Excel, this book is a valuable resource for readers who wish to acquire knowledge that can be applied to more complex systems. Visualization of the simulation results via the Visual Basic built in Microsoft EXCEL is presented as the first step towards the subject. Prior experience with the Excel add-in VBA is kept to a minimum. In addition, a chapter on quantum optimization simulation utilizing Python is added to explore the quantum computation. Readers will gain a fundamental knowledge and techniques of simulation physics, which can be extended to STEM projects and other research projects.

This book discusses the modern theory of Laplace eigenfunctions through the lens of a new tool called geodesic beams. The authors provide a brief introduction to the theory of Laplace eigenfunctions followed by an accessible treatment of geodesic beams and their applications to sup norm estimates, L^p estimates, averages, and Weyl laws. Geodesic beams have proven to be a valuable tool in the study of Laplace eigenfunctions, but their treatment is currently spread through a variety of rather technical papers. The authors present a treatment of these tools that is accessible to a wider audience of mathematicians. Readers will gain an introduction to geodesic beams and the modern theory of Laplace eigenfunctions, which will enable them to understand the cutting edge aspects of this theory.

This monograph is devoted to the study of multiscale model reduction methods from the point of view of multiscale finite element methods. Multiscale numerical methods have become popular tools for modeling processes with multiple scales. These methods allow reducing the degrees of freedom based on local offline computations. Moreover, these methods allow deriving rigorous macroscopic equations for multiscale problems without scale separation and high contrast. Multiscale methods are also used to design efficient solvers. This book offers a combination of analytical and numerical methods designed for solving multiscale problems. The book mostly focuses on methods that are based on multiscale finite element methods. Both applications and theoretical developments in this field are presented. The book is suitable for graduate students and researchers, who are interested in this topic.

Das 2-bändige Lehrbuchs vermittelt anschaulich und verständlich quanten- und festkörpertheoretische Kenntnisse und Fertigkeiten und richtet sich an Studierende der Natur- und Ingenieurswissenschaften. __Band 1 Quantenmechanik. Im ersten Teil werden ausführlich sowohl Handwerkszeug als auch Methoden erläutert, um typische Eigenwertprobleme kleinster Systeme zu lösen, wie denen des Elektrons im Kasten und des H-Atoms. Wechselwirkt Strahlung mit einem Quantensystem, kann dieses mit Schwingungen oder Rotationen antworten. Auch das Phänomen des Tunneleffekt ist nun einer Beschreibung zugänglich. Dass bei der Messung einer Eigenschaft nur ein Mittelwert, bei der einer anderen dagegen ein scharfer Wert beobachtet wird, kann nun mit absoluter Sicherheit prognostiziert werden. Der Übergang von kleinsten Systemen zu größeren atomaren oder molekularen Einheiten wie dem He-Atom, dem H2+-Ion oder dem Benzol gelingt mit Näherungsverfahren, die zufriedenstellende Übereinstimmung mit den Experimenten ermöglichen, wenn auch mit hohem Rechenaufwand. In den etwa zweihundert Aufgaben werden in den Lösungen diese Methoden ausführlich erörtert. __Band 2. Festkörperphysik. Der zweiteTeil beginnt mit der Betrachtung der einzelnen Festkörperklassen und weitet den Bogen mit der thermischen Energie und optischen Phänomenen von Isolatoren. Der Schwerpunkt liegt jedoch auf Metallen und Halbleitern, wobei mit dem Modell Freier Elektronen sowohl optische wie magnetische Effekte bis hin zum Ferromagnetismus umfassend be-schrieben werden können. Bei elektrischen Eigenschaften dagegen ist eine Ausweitung dieses Modells erforderlich, das damit aber das Fenster zu den Halbleitern öffnet, deren Eigenschaften sowohl im Volumen wie an Grenzflächen untersucht werden, so dass damit ein Verständnis von Halbleiter-bauelementen ermöglicht wird, hier dargelegt an Dioden. Viele in den über hundert Aufgaben betrachteten Fragestellungen, die von ausführlichen Lösungswe-gen begleitet sind, zeigen auf, wie weitreichend die Anwendungen sind, die sich mit der erworbenen Fertigkeit in diesem Calculus erschließen lassen.

This book treats the subject of gravitational waves (GWs) production in binary stars or black-holes and in the early universe, using tools of quantum field theory which are familiar to graduate students and researchers in particle physics. A special focus is given to the generation of templates of gravitational wave signals from Feynman diagram calculations of transition amplitudes, which interests active researchers in GWs. The book presents field theory concepts, like supersymmetry realized in spinning binaries and soft-graviton theorems, that can have practical applications in novel GW signals, like the memory effect. The book also aims at specialists in both GWs and particle physics addressing cosmological models of phase transition and inflation that can be tested in observations at terrestrial and space based interferometers, pulsar timing arrays, and the cosmic microwave anisotropy observations.

Over the course of a scientific career spanning more than fifty years, Alex Grossmann (1930-2019) made many important contributions to a wide range of areas including, among others, mathematics, numerical analysis, physics, genetics, and biology. His lasting influence can be seen not only in his research and numerous publications, but also through the relationships he cultivated with his collaborators and students. This edited volume features chapters written by some of these colleagues, as well as researchers whom Grossmann¿s work and way of thinking has impacted in a decisive way. Reflecting the diversity of his interests and their interdisciplinary nature, these chapters explore a variety of current topics in quantum mechanics, elementary particles, and theoretical physics; wavelets and mathematical analysis; and genomics and biology. A scientific biography of Grossmann, along with a more personal biography written by his son, serve as an introduction. Also included are the introduction to his PhD thesis and an unpublished paper coauthored by him. Researchers working in any of the fields listed above will find this volume to be an insightful and informative work.

This book discusses analytic and asymptotic methods relevant to radiative transfer in dilute media, such as stellar and planetary atmospheres.  Several methods, providing exact expressions for the radiation field in a semi-infinite atmosphere, are described in detail and applied to unpolarized and polarized continuous spectra and spectral lines. Among these methods, the Wiener-Hopf method, introduced in 1931 for a stellar atmospheric problem, is used today in fields such as solid mechanics, diffraction theory, or mathematical finance. Asymptotic analyses are carried out on unpolarized and polarized radiative transfer equations and on a discrete time random walk. Applicable when photons undergo a large number of scatterings, they provide criteria to distinguish between large-scale diffusive and non-diffusive behaviors, typical scales of variation of the radiation field, such as the thermalization length, and specific descriptions for regions close and far from boundaries. Its well organized synthetic view of exact and asymptotic methods of radiative transfer makes this book a valuable resource for both graduate students and professional scientists in astrophysics and beyond.

This book describes how complex systems from a variety of fields can be modeled using quantum mechanical ideas; from biology and ecology, to sociology and decision-making. Quantum mechanics is traditionally associated with microscopic systems; however, quantum concepts have also been successfully applied to a wide range of macroscopic systems both within and outside physics. The mathematical basis of these models is covered in detail, providing a self-contained and consistent approach. This book provides unique insight into the dynamics of these macroscopic systems and opens new interdisciplinary research frontiers. The authors present an essential resource for researchers in applied mathematics or theoretical physics who are interested in applying quantum mechanics to complex systems in the social, biological or ecological sciences.Describes how complex systems from a variety of fields can be modeled using quantum mechanical ideasProvides insight into the dynamics of macroscopic systems and opens new interdisciplinary research frontiersIntroduces quantum tools needed for the analysis of the dynamical behavior of macroscopic systems

This book provides the reader with a modern and comprehensive overview of nuclear polarization theory. The understanding of polarization phenomena greatly enriches data obtained from scattering and nuclear reactions by providing information on the interaction that can change spin orientation as well as important verification data for the study of nuclear structures and reaction mechanisms. The author methodically derives the polarization theory of nuclear reactions for various types of elastic scattering and two-body direct reactions between particles of different spin and unpolarized target nuclei with arbitrary spin, as well as the reactions between two polarized light particles and the polarization theory for photon beams. In addition, the polarization theories of relativistic nuclear reactions are rigorously covered in great scope and detail. A chapter on polarized particle transport theory presents the Monte-Carlo method for describing the transport of polarized particles and formalizes the polarized particle transport equation. Here, the author also illustrates a novel and concrete scheme for establishing a polarization nuclear database.Nuclear polarization is important not only for microscopic nuclear structure and reaction studies but also for nuclear engineering, applied nuclear physics, and medical physics. With the development of radioactive beam facilities and, on the theoretical side, the development of consistent microscopic nuclear reaction and structure theories, this book on the polarization theory of nuclear reactions serves as a timely source of reference for students and researchers alike.

This edited book provides invited and reviewed contributions in mathematical, physical and experimental modelling and simulations in all fluid mechanics branches. Contributions explore the emerging and state-of-the-art tools in the field authored by well-established researchers to derive improved performance of modelling and simulations. Serving the multidisciplinary fluid mechanics community, this book aims to publish new research work that enhances the prediction and understanding of fluid mechanics and balances from academic theory to practical applications through modelling, numerical studies, algorithms and simulation. The book offers researchers, students and practitioners significant insights on modelling and simulations in fluid mechanics. It offers readers a range of academic contributions on fluid mechanics by researchers that have become leaders in their field. The research work presented in this book will add values to the existing literature in terms of what needs to be done better to direct modelling and simulations towards a growing and rapidly developing field.

This book presents recent improvements in peridynamic modeling of structures. It provides sufficient theory and numerical implementation helpful to both new and existing researchers in the field.  The main focus of the book is on the non-ordinary state-based (NOSB) peridynamics (PD) and its applications for performing finite deformation. It presents the framework for modeling high stretch polymers, viscoelastic materials, thermoelasticity, plasticity, and creep. It provides a systematic derivation for dimensionally reduced structures such as axisymmetric structures and beams. Also, it presents a novel approach to impose boundary conditions without suffering from displacement kinks near the boundary. Furthermore, it presents refinements to bond-based PD model by including rotation kinematics for modeling isotropic and composite materials. Moreover, it presents a PD - FEM coupling framework in ANSYS based on principle for virtual work. Lastly, it presents an application of neural networks in the peridynamic (PINN) framework. Sample codes are provided for readers to develop hands-on experience on peridynamic modeling.  Describes new developments in peridynamics and their applications in the presence of material and geometric nonlinearity; Describes an approach to seamlessly couple PD with FE; Introduces the use of the neural network in the PD framework to solve engineering problems;Provides theory and numerical examples for researchers and students to self-study and apply in their research (Codes are provided as supplementary material);Provides theoretical development and numerical examples suitable for graduate courses.

This work presents some essential techniques that constitute the modern strategy for computing scattering amplitudes. It begins with an introductory chapter to fill the gap between a standard QFT course and the latest developments in the field. The author then tackles the main bottleneck: the computation of the loop Feynman integrals. The most efficient technique for their computation is the method of the differential equations. This is discussed in detail, with a particular focus on the mathematical aspects involved in the derivation of the differential equations and their solution. Ample space is devoted to the special functions arising from the differential equations, to their analytic properties, and to the mathematical techniques which allow us to handle them systematically.  The thesis also addresses the application of these techniques to a cutting-edge problem of importance for the physics programme of the Large Hadron Collider: five-particle amplitudes at two-loop order. It presents the first analytic results for complete two-loop five-particle amplitudes, in supersymmetric theories and QCD. The techniques discussed here open the door to precision phenomenology for processes of phenomenological interest, such as three-photon, three-jet, and di-photon + jet production.

Die Elektrodynamik wird meistens in der historisch orientierten Reihenfolge behandelt, in der das elektrische und magnetische Feld zunächst als separate Objekte eingeführt und schließlich über die Maxwell-Gleichungen miteinander verknüpft werden. Die Lorentz-Symmetrie der Theorie und die Vereinigung der beiden Felder im Feldstärketensor werden üblicherweise erst am Ende gezeigt, obwohl sich die Gleichungen dadurch vereinfachen und sie erst so in allen Bezugssystemen gelten.Damit durchläuft der Studierende zwar die historische Entwicklung, muss aber dann zum Ende der Vorlesung alles rückblickend verstehen und neu einordnen. Dieses Buch geht den umgekehrten, deduktiven Weg, der die Elektrodynamik von vornherein auf das Fundament der Speziellen Relativitätstheorie stellt und von da aus ¿ gegenüber dem üblichen Vorgehen sozusagen "rückwärts" ¿ die bekannten Phänomene und Zusammenhänge ableitet. Dieses Vorgehen erlaubt eine wesentlich straffere und ¿ was die Rolle des Elektromagnetismus im Gesamtzusammenhang der Theoretischen Physik angeht ¿ klarere Behandlung.

In the present era, many methods for modeling and qualitative analysis of various kinds of mathematical and wireless systems are available. These analyzing methods show how to use predictive computational models to acquire and analyze knowledge about these systems. The book covers real-life examples of continuous computational scenarios. This book aims to capture new developments in the mathematical modeling of systems, as well as the performance computation of wireless networks. For more details, please visit https://centralwestpublishing.com

In this modern era, communication and computation have become an integral part of each other to provide services to the common man that helps people located in any part of the world can communicate easily. The book provides future research directions and innovations in wireless communication, antenna design and computation technologies and explores the different applications of its associated technologies. In contents, the chapters on wireless communication protocols, fractal antenna designs, online learning technologies as well as technologies for post-disaster victim localization are included in the contents. The book also provides a chapter related to advanced mathematical modelling and research for disease analysis. Finally, it covers the chapter on the computation of socio-economic and demographic factors of financial literacy.For more details, please visit https://centralwestpublishing.com

This accessible and self-contained guide provides a comprehensive introduction to the popular programming language Python, with a focus on applications in chemistry and chemical physics. Ideally suited to students and researchers of chemistry learning to employ Python for problem-solving in their research, this fast-paced primer first builds a solid foundation in the programming language before progressing to advanced concepts and applications in chemistry. The required syntax and data structures are established, and then applied to solve problems computationally. Popular numerical packages are described in detail, including NumPy, SciPy, Matplotlib, SymPy, and pandas. End of chapter problems are included throughout, with worked solutions available within the book. Additional resources, datasets, and Jupyter Notebooks are provided on a companion website, allowing readers to reinforce their understanding and gain confidence applying their knowledge through a hands-on approach.

This book includes contributions about mathematics, physics, philosophy of science, economics and finance and resulted from the Summer School "e;Complexity and Emergence: Ideas, Methods, with a Special Attention to Economics and Finance"e; held in Lake Como School of Advanced Studies, on 22-27 July 2018.The aim of the book is to provide useful instruments from the theory of complex systems, both on the theoretical level and the methodological ones, profiting from knowledge and insights from leading experts of different communities. It moves from the volume editors' conviction that to achieve progress in understanding socio-economical as well as ecological problems of our complex word such preparation is needed, together with a critical reconsideration of our basic scientific and economical approach.The potential readers are primarily master and doctorate students of mathematics, information sciences, theoretical physics and economics, as well as research workers in those areas, who want to enlarge their spectrum of knowledge towards the area of complexity and emergence. Since ideas and methods of the theory of complex systems also apply to other areas (from engineering and architecture to biology and medicine, e.g.), students and research workers from those areas will also profit from this book.

This book presents a modern view of anomalies in quantum field theories. It is divided into six parts. The first part is preparatory covering an introduction to fermions, a description of the classical symmetries, and a short introduction to conformal symmetry. The second part of the book is devoted to the relation between anomalies and cohomology. The third part deals with perturbative methods to compute gauge, diffeomorphism and trace anomalies. In the fourth part the same anomalies are calculated with non-perturbative heat-kernel-like methods. Part five is devoted to the family's index theorem and its application to chiral anomalies, and to the differential characters and their applications to global anomalies. Part six is devoted to special topics including a complete calculation of trace and diffeomorphism anomalies of a Dirac fermion in a MAT background in two dimensions, Wess-Zumino terms in field theories, sigma models, their local and global anomalies and their cancelation, and finally the analysis of the worldsheet, sigma model, and target space anomalies of string and superstring theories.The book is targeted to researchers and graduate students.

¿Mangalyaan was launched on November 5, 2013, to Mars by Indian Space Research Organization (ISRO). On October 2, 2022, ISRO declared that Mangalyaan had lost communications with Earth. Mars Color Camera (MCC) on-board Mangalyaan has taken thousands pictures of Mars. A full disk of Mars image observed by Viking is shown on the cover page of this book. Mars is covered by the dust as observed by Mangalyaan (from Arya et al., 2015). This book presents the atmospheric and ionospheric results obtained from all missions to Mars. It also covers various atmospheric and ionospheric models of Mars. Broadly speaking, the planet¿s atmosphere can be divided into two regions: lower and upper. These two regions can be coupled due to the propagation of energy from the lower to the upper atmosphere. The first-ever book on the aeronomy of Mars, this work is intended to help students and researchers familiarize themselves with the field of aeronomy. In addition, it helps planetary probe designers, engineers, and other users in the scientific community, e.g., planetary geologists and geophysicists¿.

This book includes problems based on the material in the course of physical kinetics for the students of general and applied physics. It contains 60 problems with detailed solutions. The comments to the problems reflect the connection with the problems and methods of modern physical kinetics. A brief introduction gives the necessary information for solving and understanding the problems. The book is proposed for students and postgraduates studying the theoretical physics. The book is used as a supplement to the textbooks published on physical kinetics. The purpose of the book is to help students in training the practical skills and mastering the basic elements of physical kinetics. To understand the subject matter, it is sufficient to know the traditional courses of theoretical physics.

This text describes a comprehensive adjoint sensitivity analysis methodology (nth-CASAM), developed by the author, which enablesthe efficient and exact computation of arbitrarily high-order functional derivatives of model responses to model parameters in large-scale systems. The nth-CASAM framework is set in linearly increasing Hilbert spaces, each of state-function-dimensionality, as opposed to exponentially increasing parameter-dimensional spaces, thereby overcoming the so-called ¿curse of dimensionality¿ in sensitivity and uncertainty analysis. The nth-CASAM is applicable to any model; the larger the number of model parameters, the more efficient the nth-CASAM becomes for computing arbitrarily high-order response sensitivities. The book will be helpful to those working in the fields of sensitivity analysis, uncertainty quantification, model validation, optimization, data assimilation, model calibration, sensor fusion, reduced-order modelling, inverse problems and predictive modelling.This Volume Two, the second of three, presents the large-scale application of the nth-CASAM to perform a representative fourth-order sensitivity analysis of the Polyethylene-Reflected Plutonium benchmark described in the Nuclear Energy Agency (NEA) International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook. This benchmark is modeled mathematically by the Boltzmann particle transport equation, involving 21,976 imprecisely-known parameters, the numerical solution of which requires representative large-scale computations. The sensitivity analysis presented in this volume is the most comprehensive ever performed in the field of reactor physics and the results presented in this book prove, perhaps counter-intuitively, that many of the 4th-order sensitivities are much larger than the corresponding 3rd-order ones, which are, in turn, much larger than the 2nd-order ones, all of which are much larger than the 1st-order sensitivities. Currently, the nth-CASAM is the only known methodology which enables such large-scale computations of exactly obtained expressions of arbitrarily-high-order response sensitivities.