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Author: H. M. Fried
Publisher: Cambridge University Press
ISBN: 1139433059
Category : Science
Languages : en
Pages : 183
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Book Description
This book presents a functional approach to the construction, use and approximation of Green's functions and their associated ordered exponentials. After a brief historical introduction, the author discusses new solutions to problems involving particle production in crossed laser fields and non-constant electric fields. Applications to problems in potential theory and quantum field theory are covered, along with approximations for the treatment of color fluctuations in high-energy QCD scattering, and a model for summing classes of eikonal graphs in high-energy scattering problems. The book also presents a variant of the Fradkin representation which suggests a new non-perturbative approximation scheme, and provides a qualitative measure of the error involved in each such approximation. Covering the basics as well as more advanced applications, this book is suitable for graduate students and researchers in a wide range of fields, including quantum field theory, fluid dynamics and applied mathematics.
Author: H. M. Fried
Publisher: Cambridge University Press
ISBN: 1139433059
Category : Science
Languages : en
Pages : 183
Get Book Here
Book Description
This book presents a functional approach to the construction, use and approximation of Green's functions and their associated ordered exponentials. After a brief historical introduction, the author discusses new solutions to problems involving particle production in crossed laser fields and non-constant electric fields. Applications to problems in potential theory and quantum field theory are covered, along with approximations for the treatment of color fluctuations in high-energy QCD scattering, and a model for summing classes of eikonal graphs in high-energy scattering problems. The book also presents a variant of the Fradkin representation which suggests a new non-perturbative approximation scheme, and provides a qualitative measure of the error involved in each such approximation. Covering the basics as well as more advanced applications, this book is suitable for graduate students and researchers in a wide range of fields, including quantum field theory, fluid dynamics and applied mathematics.
Author: Peter Kopietz
Publisher: Springer Science & Business Media
ISBN: 364205093X
Category : Language Arts & Disciplines
Languages : en
Pages : 383
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Book Description
This book, based on a graduate course given by the authors, is a pedagogic and self-contained introduction to the renormalization group with special emphasis on the functional renormalization group. The functional renormalization group is a modern formulation of the Wilsonian renormalization group in terms of formally exact functional differential equations for generating functionals. In Part I the reader is introduced to the basic concepts of the renormalization group idea, requiring only basic knowledge of equilibrium statistical mechanics. More advanced methods, such as diagrammatic perturbation theory, are introduced step by step. Part II then gives a self-contained introduction to the functional renormalization group. After a careful definition of various types of generating functionals, the renormalization group flow equations for these functionals are derived. This procedure is shown to encompass the traditional method of the mode elimination steps of the Wilsonian renormalization group procedure. Then, approximate solutions of these flow equations using expansions in powers of irreducible vertices or in powers of derivatives are given. Finally, in Part III the exact hierarchy of functional renormalization group flow equations for the irreducible vertices is used to study various aspects of non-relativistic fermions, including the so-called BCS-BEC crossover, thereby making the link to contemporary research topics.
Author: Ardeshir Guran
Publisher: World Scientific
ISBN: 9814499099
Category : Technology & Engineering
Languages : en
Pages : 415
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Book Description
This book is a collection of papers on electromagnetic wave mechanics and its applications written by experts in this field. It offers the reader a sampling of exciting research areas in this field. The topics include polarimetric imaging, radar spectroscopy, surface or creeping waves, bistatic radar scattering, the Seebeck affect. Mathematical methods include inverse scattering theory, singularity expansion method, mixed potential integral equation, method of moments, and diffraction theory. Applications include Cellular Mobile Radios (CMR), radar target identification, and Personal Communication Services (PCS). This book shows how electromagnetic wave theory is currently being utilized and investigated. It involves a modicom of mathematical physics and will be of interest to researchers and graduate students in electrical engineering, physics and applied mathematics.
Author: Bertrand M. Roehner
Publisher: Cambridge University Press
ISBN: 1139432346
Category : Business & Economics
Languages : en
Pages : 250
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Book Description
The main objective of this 2002 book is to show that behind the bewildering diversity of historical speculative episodes it is possible to find hidden regularities, thus preparing the way for a unified theory of market speculation. Speculative bubbles require the study of various episodes in order for a comparative perspective to be obtained and the analysis developed in this book follows a few simple but unconventional ideas. Investors are assumed to exhibit the same basic behavior during speculative episodes whether they trade stocks, real estate, or postage stamps. The author demonstrates how some of the basic concepts of dynamical system theory, such as the notions of impulse response, reaction times and frequency analysis, play an instrumental role in describing and predicting speculative behavior. This book will serve as a useful introduction for students of econophysics, and readers with a general interest in economics as seen from the perspective of physics.
Author: Herbert Martin Fried
Publisher: World Scientific
ISBN: 9814415901
Category : Science
Languages : en
Pages : 281
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Book Description
These pages offer a simple, analytic, functional approach to non-perturbative QFT, using a frequently overlooked functional representation of Fradkin to explicitly calculate relevant portions of the Schwinger Generating Functional (GF). In QED, this corresponds to summing all Feynman graphs representing virtual photon exchange between charged particles. It is then possible to see, analytically, the cancellation of an infinite number of perturbative, UV logarithmic divergences, leading to an approximate but most reasonable statement of finite charge renormalization.A similar treatment of QCD, with the addition of a long-overlooked but simple rearrangement of the Schwinger GF which displays Manifest Gauge Invariance, is then able to produce a simple, analytic derivation of quark-binding potentials without any approximation of infinite quark masses. A crucial improvement of previous QCD theory takes into account the experimental fact that asymptotic quarks are always found in bound states; and therefore that their transverse coordinates can never be measured, nor specified, exactly. And this change of formalism permits a clear and simple realization of true quark binding, into mesons and nucleons. An extension into the QCD binding of two nucleons into an effective deuteron presents a simple, analytic derivation of nuclear forces.Finally, a new QED-based solution of Vacuum Energy is displayed as a possible candidate for Dark Energy. An obvious generalization to include Inflation, which automatically suggests a model for Dark Matter, is immediately possible; and one more obvious generalization produces an understanding of the origin of the Big Bang, and of the Birth (and Death) of a Universe. If nothing else, this illustrates the Power and the Reach of Quantum Field Theory.
Author: Charles Paul Enz
Publisher: World Scientific
ISBN: 9789971503369
Category : Science
Languages : en
Pages : 448
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Book Description
The main aim of this book is to give a self-contained and representative cross section through present-day research in solid-state physics. This covers metallic and mesoscopic transport, localization by disorder and superconductivity, including questions related to high-temperature superconductors and to heavy fermion systems. An important part of the book is devoted to itinerant-electron magnetism, discussing paramagnons, strong correlation, magnetization fluctuations and spin density waves. All the formal tools used in these chapters are developed in the first part of the book which contains a thorough discussion of second quantization and of perturbation theory for an arbitrary complex time path and also describes the functional approach to Feynman diagrams including general ward identities. Each chapter contains an extensive list of the relevant literature and a series of problems with detailed solutions which complement the main text. The book is meant both as a course and a research tool.
Author: Andrei D. Polyanin
Publisher: CRC Press
ISBN: 0203881052
Category : Mathematics
Languages : en
Pages : 1143
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Book Description
Unparalleled in scope compared to the literature currently available, the Handbook of Integral Equations, Second Edition contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equa
Author: Carlo Di Castro
Publisher: Cambridge University Press
ISBN: 1107039401
Category : Science
Languages : en
Pages : 549
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Book Description
An innovative and modular textbook combining established classical topics in statistical mechanics with the latest developments in condensed matter physics.
Author: Shantanu Das
Publisher: Cambridge Scholars Publishing
ISBN: 1527547116
Category : Mathematics
Languages : en
Pages : 533
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Book Description
This book presents a simplified deliberation of fractional calculus, which will appeal not only to beginners, but also to various applied science mathematicians and engineering researchers. The text develops the ideas behind this new field of mathematics, beginning at the most elementary level, before discussing its actual applications in different areas of science and engineering. This book shows that the simple, classical laws based on Newtonian calculus, which work quite well under limiting and idealized conditions, are not of much use in describing the dynamics of actual systems. As such, the application of non-Newtonian, or generalized, calculus in the governing equations, allows the order of differentiation and integration to take on non-integer values.
Author: G. Rickayzen
Publisher: Courier Corporation
ISBN: 048631586X
Category : Science
Languages : en
Pages : 370
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Book Description
Presentation of the basic theoretical formulation of Green's functions, followed by specific applications: transport coefficients of a metal, Coulomb gas, Fermi liquids, electrons and phonons, superconductivity, superfluidity, and magnetism. 1984 edition.
