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A Theory Of Fields

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A Theory of Fields

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A Theory of Fields by Neil Fligstein,Doug McAdam Book Summary:

Finding ways to understand the nature of social change and social order-from political movements to market meltdowns-is one of the enduring problems of social science.A Theory of Fields draws together far-ranging insights from social movement theory, organizational theory, and economic and political sociology to construct a general theory of social organization and strategic action. In a work of remarkable synthesis, imagination, and analysis, Neil Fligstein and Doug McAdam propose that social change and social order can be understood through what they call strategic action fields. They posit that these fields are the general building blocks of political and economic life, civil society, and the state, and the fundamental form of order in our world today. Similar to Russian dolls, they are nested and connected in a broader environment of almost countless proximate and overlapping fields. Fields are mutually dependent; change in one often triggers change in another. At the core of the theory is an account of how social actors fashion and maintain order in a given field. This sociological theory of action, what they call "social skill," helps explain what individuals do in strategic action fields to gain cooperation or engage in competition. To demonstrate the breadth of the theory, Fligstein and McAdam make its abstract principles concrete through extended case studies of the Civil Rights Movement and the rise and fall of the market for mortgages in the U.S. since the 1960s. The book also provides a "how-to" guide to help others implement the approach and discusses methodological issues. With a bold new approach, A Theory of Fields offers both a rigorous and practically applicable way of thinking through and making sense of social order and change-and how one emerges from the other-in modern, complex societies.

Bourdieu's Theory of Social Fields

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Bourdieu's Theory of Social Fields by Mathieu Hilgers,Eric Mangez Book Summary:

Bourdieu’s theory of social fields is one of his key contributions to social sciences and humanities. However, it has never been subjected to genuine critical examination. This book fills that gap and offers a clear and wide-ranging introduction to the theory. It includes a critical discussion of its methodology and relevance in different subject areas in the social sciences and humanities. Part I "theoretical investigations" offers a theoretical account of the theory, while also identifying some of its limitations and discussing several strategies to overcome them. Part II "Education, culture and organization" presents the theory at work and highlights its advantages and disadvantages. The focus in Part III devoted to "The State" is on the formation and evolution of the State and public policy in different contexts. The chapters show the usefulness of field theory in describing, explaining and understanding the functioning of the State at different stages in its historical trajectory including its recent redefinition with the advent of the neoliberal age. A last chapter outlines a postcolonial use of the theory of fields.

The Quantum Theory of Fields

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The Quantum Theory of Fields by Steven Weinberg,Weinberg S Book Summary:

Comprehensive introduction to quantum field theory by Nobel Laureate Steven Weinberg, now available in paperback.

War in Social Thought

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War in Social Thought by Hans Joas,Wolfgang Knöbl Book Summary:

Argues that sociologists have either ignored or grappled with the idea of war and examines the reasons behind this denial of the violent nature of the human race.

The Classical Theory of Fields

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The Classical Theory of Fields by L D Landau,Lev Davydovič Landau (Physicien, Union Soviétique),Евгений Михайлович Лифшиц Book Summary:

The fourth edition contains seven new sections with chapters on General Relativity, Gravitational Waves and Relativistic Cosmology. The text has been thoroughly revised and additional problems inserted. The Complete course of Theoretical Physics by Landau and Lifshitz, recognized as two of the world's outstanding physicists, is published in full by Butterworth-Heinemann. It comprises nine volumes, covering all branches of the subject; translations from the Russian are by leading scientists.

Quantum Theory of Fields

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Quantum Theory of Fields by Gregor Wentzel Book Summary:

Written by a pioneer of quantum field theory, this introductory volume explores scalar fields, vector meson fields, quantum electrodynamics, quantization of electron wave field according to exclusion principle. 1949 edition.

Electrodynamics and Classical Theory of Fields and Particles

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Electrodynamics and Classical Theory of Fields and Particles by A. O. Barut Book Summary:

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.

The Quantum Theory of Fields: Volume 1, Foundations

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The Quantum Theory of Fields: Volume 1, Foundations by Steven Weinberg Book Summary:

Available for the first time in paperback, The Quantum Theory of Fields is a self-contained, comprehensive, and up-to-date introduction to quantum field theory from Nobel Laureate Steven Weinberg. Volume I introduces the foundations of quantum field theory. The development is fresh and logical throughout, with each step carefully motivated by what has gone before. After a brief historical outline, the book begins with the principles of relativity and quantum mechanics, and the properties of particles that follow. Quantum field theory emerges from this as a natural consequence. The classic calculations of quantum electrodynamics are presented in a thoroughly modern way, showing the use of path integrals and dimensional regularization. It contains much original material, and is peppered with examples and insights drawn from the author's experience as a leader of elementary particle research. Exercises are included at the end of each chapter.

The Classical Theory of Fields

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The Classical Theory of Fields by Carl S. Helrich Book Summary:

The study of classical electromagnetic fields is an adventure. The theory is complete mathematically and we are able to present it as an example of classical Newtonian experimental and mathematical philosophy. There is a set of foundational experiments, on which most of the theory is constructed. And then there is the bold theoretical proposal of a field-field interaction from James Clerk Maxwell. This textbook presents the theory of classical fields as a mathematical structure based solidly on laboratory experiments. Here the student is introduced to the beauty of classical field theory as a gem of theoretical physics. To keep the discussion fluid, the history is placed in a beginning chapter and some of the mathematical proofs in the appendices. Chapters on Green’s Functions and Laplace’s Equation and a discussion of Faraday’s Experiment further deepen the understanding. The chapter on Einstein’s relativity is an integral necessity to the text. Finally, chapters on particle motion and waves in a dispersive medium complete the picture. High quality diagrams and detailed end-of-chapter questions enhance the learning experience.

The Class Ceiling

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The Class Ceiling by Friedman, Sam,Laurison, Daniel Book Summary:

Politicians continually tell us that anyone can get ahead. But is that really true? This important best-selling book takes readers behind the closed doors of elite employers to reveal how class affects who gets to the top. Friedman and Laurison show that a powerful ‘class pay gap’ exists in Britain’s elite occupations. Even when those from working-class backgrounds make it into prestigious jobs, they earn, on average, 16% less than colleagues from privileged backgrounds. But why is this the case? . Drawing on 175 interviews across four case studies - television, accountancy, architecture, and acting – they explore the complex barriers facing the upwardly mobile. This is a rich, ambitious book that demands we take seriously not just the glass but also the class ceiling.

Are We There Yet? The Search for a Theory of Everything

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Are We There Yet? The Search for a Theory of Everything by Moataz H. Emam Book Summary:

We live in exciting times. the frontiers of physics have been pushed to unprecedented horizons. the Holy Grail of fundamental physics research today is to find and describe a theory that explains, at least in principle, all physical phenomena, which in turns explains chemistry, biology and other material sciences. This, however, is not without controversy. the current candidate for such a theory is known as string or superstring theory. It suffers from the problem of being a purely mathematical science with no experimental backing and belief in it has been criticized as bordering on "faith" as opposed to scientific scrutiny. On the other hand the recent switching-on of our most advanced experimental tool, the Large Hadron Collider in Switzerland, gives new hope in our search for clues as to what the universe is made of on a fundamental level. What happened exactly on, or even before, the Big Bang? Where are we coming from and where are we going? Questions that have never been addressed before by physicists. the game is afoot and the search is on. This book contains articles by leading physicists describing the current situation. Among them are proponents as well as opponents of string theory, proponents of other ideas, and experimentalists.

Classical Theory of Gauge Fields

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Classical Theory of Gauge Fields by Valery Rubakov Book Summary:

Based on a highly regarded lecture course at Moscow State University, this is a clear and systematic introduction to gauge field theory. It is unique in providing the means to master gauge field theory prior to the advanced study of quantum mechanics. Though gauge field theory is typically included in courses on quantum field theory, many of its ideas and results can be understood at the classical or semi-classical level. Accordingly, this book is organized so that its early chapters require no special knowledge of quantum mechanics. Aspects of gauge field theory relying on quantum mechanics are introduced only later and in a graduated fashion--making the text ideal for students studying gauge field theory and quantum mechanics simultaneously. The book begins with the basic concepts on which gauge field theory is built. It introduces gauge-invariant Lagrangians and describes the spectra of linear perturbations, including perturbations above nontrivial ground states. The second part focuses on the construction and interpretation of classical solutions that exist entirely due to the nonlinearity of field equations: solitons, bounces, instantons, and sphalerons. The third section considers some of the interesting effects that appear due to interactions of fermions with topological scalar and gauge fields. Mathematical digressions and numerous problems are included throughout. An appendix sketches the role of instantons as saddle points of Euclidean functional integral and related topics. Perfectly suited as an advanced undergraduate or beginning graduate text, this book is an excellent starting point for anyone seeking to understand gauge fields.

The Architecture of Markets

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The Architecture of Markets by Neil Fligstein Book Summary:

This work seeks to make sense of modern capitalism by developing a sociological theory of market institutions. Addressing the dynamism that capitalism brings with it, the author argues that the basic drift of any one market and it's actors, even allowing for competition, is toward stabilization.

Introduction to the Classical Theory of Particles and Fields

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Introduction to the Classical Theory of Particles and Fields by Boris Kosyakov Book Summary:

This volume is intended as a systematic introduction to gauge field theory for advanced undergraduate and graduate students in high energy physics. The discussion is restricted to the classical (non-quantum) theory in Minkowski spacetime. Particular attention has been given to conceptual aspects of field theory, accurate definitions of basic physical notions, and thorough analysis of exact solutions to the equations of motion for interacting systems.

Topics in the Theory of Algebraic Function Fields

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Topics in the Theory of Algebraic Function Fields by Gabriel Daniel Villa Salvador Book Summary:

The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory of numbers. The examination explains both the similarities and fundamental differences between function fields and number fields, including many exercises and examples to enhance understanding and motivate further study. The only prerequisites are a basic knowledge of field theory, complex analysis, and some commutative algebra.

The Conceptual Framework of Quantum Field Theory

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The Conceptual Framework of Quantum Field Theory by Anthony Duncan Book Summary:

The book provides a step by step construction of the framework of relativistic quantum field theory, starting from a minimal set of basic foundational postulates. The emphasis is on a careful and detailed description of the conceptual subtleties of modern field theory, many of which are glossed over in other texts.

Lectures on Classical and Quantum Theory of Fields

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Lectures on Classical and Quantum Theory of Fields by Henryk Arodz,Leszek Hadasz Book Summary:

This textbook addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. It aims to deliver a unique combination of classical and quantum field theory in one compact course.

Model Theory of Fields

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Model Theory of Fields by David Marker,Margit Messmer,Anand Pillay Book Summary:

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the fifth publication in the Lecture Notes in Logic series, the authors give an insightful introduction to the fascinating subject of the model theory of fields, concentrating on its connections to stability theory. In the first two chapters David Marker gives an overview of the model theory of algebraically closed, real closed and differential fields. In the third chapter Anand Pillay gives a proof that there are 2א non-isomorphic countable differential closed fields. Finally, Margit Messmer gives a survey of the model theory of separably closed fields of characteristic p > 0.

The Quantum Theory of Fields: Volume 1, Foundations

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The Quantum Theory of Fields: Volume 1, Foundations by Steven Weinberg Book Summary:

Available for the first time in paperback, The Quantum Theory of Fields is a self-contained, comprehensive, and up-to-date introduction to quantum field theory from Nobel Laureate Steven Weinberg. Volume I introduces the foundations of quantum field theory. The development is fresh and logical throughout, with each step carefully motivated by what has gone before. After a brief historical outline, the book begins with the principles of relativity and quantum mechanics, and the properties of particles that follow. Quantum field theory emerges from this as a natural consequence. The classic calculations of quantum electrodynamics are presented in a thoroughly modern way, showing the use of path integrals and dimensional regularization. It contains much original material, and is peppered with examples and insights drawn from the author's experience as a leader of elementary particle research. Exercises are included at the end of each chapter.

Handbook of Contemporary Sociological Theory

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Handbook of Contemporary Sociological Theory by Seth Abrutyn Book Summary:

This Handbook provides the hidden common threads that tie sociological inquiry together and featuring eminent scholars, it separates itself from its predecessors in substance and organization. Rather than rehashing old debates or longingly gazing at the past, this book presents sociologists with new ways of conceptualizing the organization and presentation of sociological theory. At the heart of this Handbook’s vision is the twin goals of making theory a viable enterprise by reconceptualizing how we teach theory and keeping theory closely tied to its empirical applications. Three strategies are offered: (1) Elucidating how classic issues like integration or interaction are interrogated today; (2) Presenting a coherent vision of the social levels of reality that theorists work on such as communities, groups, and the self as well as how the coherence of these levels speaks to the macro-micro link; and, (3) Theorizing the social world rather than celebrating theorists or theories; that is, one can look at how theory is used holistically to understand the constraints the social world places on our lived experience or the dynamics of social change. Hence, in the second decade of the 21st century, it has become clear that sociology is at a crossroads as the number of theorists and amount of theory available is increasingly unmanageable and unknowable by the vast majority of professionals and students. As such, this Handbook of Contemporary Sociological Theory presents the novice and the expert with the a roadmap for traversing this crossroad and building a more coherent, robust, and cumulative sociology.

Social Movements and Organization Theory

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Social Movements and Organization Theory by Gerald F. Davis,Doug McAdam,W. Richard Scott,Mayer N. Zald Book Summary:

Although the fields of organization theory and social movement theory have long been viewed as belonging to different worlds, recent events have intervened, reminding us that organizations are becoming more movement-like - more volatile and politicized - while movements are more likely to borrow strategies from organizations. Organization theory and social movement theory are two of the most vibrant areas within the social sciences. This collection of original essays and studies both calls for a closer connection between these fields and demonstrates the value of this interchange. Three introductory, programmatic essays by leading scholars in the two fields are followed by eight empirical studies that directly illustrate the benefits of this type of cross-pollination. The studies variously examine the processes by which movements become organized and the role of movement processes within and among organizations. The topics covered range from globalization and transnational social movement organizations to community recycling programs.

Waves, Particles and Fields

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Waves, Particles and Fields by Anthony C. Fischer-Cripps Book Summary:

This book fills a gap in the middle ground between quantum mechanics of a single electron to the concept of a quantum field. In doing so, the book is divided into two parts; the first provides the necessary background to quantum theory extending from Planck’s formulation of black body radiation to Schrodinger’s equation; and the second part explores Dirac’s relativistic electron to quantum fields, finishing with an description of Feynman diagrams and their meaning. Much more than a popular account, yet not too heavy so as to be inaccessible, this book assumes no prior knowledge of quantum physics or field theory and provides the necessary foundations for readers to then progress to more advanced texts on quantum field theory. It will be of interest to undergraduate students in physics and mathematics, in addition to an interested, general audience. Features: Provides an extensive yet accessible background to the concepts Contains numerous, illustrative diagrams Presents in-depth explanations of difficult subjects

Social Structures

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Social Structures by John Levi Martin Book Summary:

Social Structures is a book that examines how structural forms spontaneously arise from social relationships. Offering major insights into the building blocks of social life, it identifies which locally emergent structures have the capacity to grow into larger ones and shows how structural tendencies associated with smaller structures shape and constrain patterns of larger structures. The book then investigates the role such structures have played in the emergence of the modern nation-state. Bringing together the latest findings in sociology, anthropology, political science, and history, John Levi Martin traces how sets of interpersonal relationships become ordered in different ways to form structures. He looks at a range of social structures, from smaller ones like families and street gangs to larger ones such as communes and, ultimately, nation-states. He finds that the relationships best suited to forming larger structures are those that thrive in conditions of inequality; that are incomplete and as sparse as possible, and thereby avoid the problem of completion in which interacting members are required to establish too many relationships; and that abhor transitivity rather than assuming it. Social Structures argues that these "patronage" relationships, which often serve as means of loose coordination in the absence of strong states, are nevertheless the scaffolding of the social structures most distinctive to the modern state, namely the command army and the political party.

Extremes in Random Fields

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Extremes in Random Fields by Benjamin Yakir Book Summary:

Presents a useful new technique for analyzing theextreme-value behaviour of random fields Modern science typically involves the analysis of increasinglycomplex data. The extreme values that emerge in the statisticalanalysis of complex data are often of particular interest. Thisbook focuses on the analytical approximations of the statisticalsignificance of extreme values. Several relatively complexapplications of the technique to problems that emerge in practicalsituations are presented. All the examples are difficult toanalyze using classical methods, and as a result, the authorpresents a novel technique, designed to be more accessible to theuser. Extreme value analysis is widely applied in areas such asoperational research, bioinformatics, computer science, finance andmany other disciplines. This book will be useful for scientists,engineers and advanced graduate students who need to develop theirown statistical tools for the analysis of their data. Whilst thisbook may not provide the reader with the specific answer it willinspire them to rethink their problem in the context of randomfields, apply the method, and produce a solution.

Theory of Interacting Quantum Fields

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Theory of Interacting Quantum Fields by Alexei L. Rebenko Book Summary:

This monograph is devoted to the systematic and encyclopedic presentation of the foundations of quantum field theory. It represents mathematical problems of the quantum field theory with regard to the new methods of the constructive and Euclidean field theory formed for the last thirty years of the 20th century on the basis of rigorous mathematical tools of the functional analysis, the theory of operators, and the theory of generalized functions. The book is useful for young scientists who desire to understand not only the formal structure of the quantum field theory but also its basic concepts and connection with classical mechanics, relativistic classical field theory, quantum mechanics, group theory, and the theory of functional integration.

Quantum Field Theory in Curved Spacetime

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Quantum Field Theory in Curved Spacetime by Leonard Parker,David Toms Book Summary:

Quantum field theory in curved spacetime has been remarkably fruitful. It can be used to explain how the large-scale structure of the universe and the anisotropies of the cosmic background radiation that we observe today first arose. Similarly, it provides a deep connection between general relativity, thermodynamics, and quantum field theory. This book develops quantum field theory in curved spacetime in a pedagogical style, suitable for graduate students. The authors present detailed, physically motivated, derivations of cosmological and black hole processes in which curved spacetime plays a key role. They explain how such processes in the rapidly expanding early universe leave observable consequences today, and how in the context of evaporating black holes, these processes uncover deep connections between gravitation and elementary particles. The authors also lucidly describe many other aspects of free and interacting quantized fields in curved spacetime.

Quantum Field Theory and the Standard Model

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Quantum Field Theory and the Standard Model by Matthew D. Schwartz Book Summary:

Modern introduction to quantum field theory for graduates, providing intuitive, physical explanations supported by real-world applications and homework problems.

Condensed Matter Field Theory

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Condensed Matter Field Theory by Alexander Altland,Ben D. Simons Book Summary:

Modern experimental developments in condensed matter and ultracold atom physics present formidable challenges to theorists. This book provides a pedagogical introduction to quantum field theory in many-particle physics, emphasizing the applicability of the formalism to concrete problems. This second edition contains two new chapters developing path integral approaches to classical and quantum nonequilibrium phenomena. Other chapters cover a range of topics, from the introduction of many-body techniques and functional integration, to renormalization group methods, the theory of response functions, and topology. Conceptual aspects and formal methodology are emphasized, but the discussion focuses on practical experimental applications drawn largely from condensed matter physics and neighboring fields. Extended and challenging problems with fully worked solutions provide a bridge between formal manipulations and research-oriented thinking. Aimed at elevating graduate students to a level where they can engage in independent research, this book complements graduate level courses on many-particle theory.

Quantum Theory of Fields

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Quantum Theory of Fields by Gregor Wentzel Book Summary:

Written by a pioneer of quantum field theory, this introductory volume explores scalar fields, vector meson fields, quantum electrodynamics, quantization of electron wave field according to exclusion principle. 1949 edition.

Symbolic Power, Politics, and Intellectuals

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Symbolic Power, Politics, and Intellectuals by David L. Swartz Book Summary:

Power is the central organizing principle of all social life, from culture and education to stratification and taste. And there is no more prominent name in the analysis of power than that of noted sociologist Pierre Bourdieu. Throughout his career, Bourdieu challenged the commonly held view that symbolic power—the power to dominate—is solely symbolic. He emphasized that symbolic power helps create and maintain social hierarchies, which form the very bedrock of political life. By the time of his death in 2002, Bourdieu had become a leading public intellectual, and his argument about the more subtle and influential ways that cultural resources and symbolic categories prevail in power arrangements and practices had gained broad recognition. In Symbolic Power, Politics, and Intellectuals, David L. Swartz delves deeply into Bourdieu’s work to show how central—but often overlooked—power and politics are to an understanding of sociology. Arguing that power and politics stand at the core of Bourdieu’s sociology, Swartz illuminates Bourdieu’s political project for the social sciences, as well as Bourdieu’s own political activism, explaining how sociology is not just science but also a crucial form of political engagement.

The Structure of Field Space

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The Structure of Field Space by N.A Book Summary:

Download or read The Structure of Field Space book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc).

Gaussian Markov Random Fields

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Gaussian Markov Random Fields by Havard Rue,Leonhard Held Book Summary:

Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studie

A Theory of Natural Philosophy

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A Theory of Natural Philosophy by Ruggero Giuseppe Boscovich,J M Child Book Summary:

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

The Potential of Fields in Einstein's Theory of Gravitation

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The Potential of Fields in Einstein's Theory of Gravitation by Zafar Ahsan Book Summary:

This book presents a detailed study of the Lanczos potential in general relativity by using tetrad formalisms. It demonstrates that these formalisms offer some simplifications over the tensorial methods, and investigates a general approach to finding the Lanczos potential for algebraic space–time by translating all the tensorial relations concerning the Lanczos potential into the language of tetrad formalisms and using the Newman–Penrose and Geroch–Held–Penrose formalisms. In addition, the book obtains the Lanczos potential for perfect fluid space–time, and applies the results to cosmological models of the universe. In closing, it highlights other methods, apart from tetrad formalisms, for finding the Lanczos potential, as well as further applications of the Newman–Penrose formalism. Given its scope, the book will be of interest to pure mathematicians, theoretical physicists and cosmologists, and will provide common ground for communication among these scientific communities.

Quantum Theory of Many-variable Systems and Fields

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Quantum Theory of Many-variable Systems and Fields by B. Sakita Book Summary:

These lecture notes are based on special courses on Field Theory and Statistical Mechanics given for graduate students at the City College of New York. It is an ideal text for a one-semester course on Quantum Field Theory.

A Course in Theoretical Physics

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A Course in Theoretical Physics by P. John Shepherd Book Summary:

This book is a comprehensive account of five extended modules covering the key branches of twentieth-century theoretical physics, taught by the author over a period of three decades to students on bachelor and master university degree courses in both physics and theoretical physics. The modules cover nonrelativistic quantum mechanics, thermal and statistical physics, many-body theory, classical field theory (including special relativity and electromagnetism), and, finally, relativistic quantum mechanics and gauge theories of quark and lepton interactions, all presented in a single, self-contained volume. In a number of universities, much of the material covered (for example, on Einstein’s general theory of relativity, on the BCS theory of superconductivity, and on the Standard Model, including the theory underlying the prediction of the Higgs boson) is taught in postgraduate courses to beginning PhD students. A distinctive feature of the book is that full, step-by-step mathematical proofs of all essential results are given, enabling a student who has completed a high-school mathematics course and the first year of a university physics degree course to understand and appreciate the derivations of very many of the most important results of twentieth-century theoretical physics.