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Graphs in Perturbation Theory by Michael Borinsky Pdf
This book is the first systematic study of graphical enumeration and the asymptotic algebraic structures in perturbative quantum field theory. Starting with an exposition of the Hopf algebra structure of generic graphs, it reviews and summarizes the existing literature. It then applies this Hopf algebraic structure to the combinatorics of graphical enumeration for the first time, and introduces a novel method of asymptotic analysis to answer asymptotic questions. This major breakthrough has combinatorial applications far beyond the analysis of graphical enumeration. The book also provides detailed examples for the asymptotics of renormalizable quantum field theories, which underlie the Standard Model of particle physics. A deeper analysis of such renormalizable field theories reveals their algebraic lattice structure. The pedagogical presentation allows readers to apply these new methods to other problems, making this thesis a future classic for the study of asymptotic problems in quantum fields, network theory and far beyond.
Large-Order Behaviour of Perturbation Theory by J.C. Le Guillou,J. Zinn-Justin Pdf
This volume is concerned with the determination of the behaviour of perturbation theory at large orders in quantum mechanics and quantum field theory, and its application to the problem of summation of perturbation series. Perturbation series in quantum field theory and in many quantum mechanics models are only asymptotic and thus diverge for all values of the expansion parameter. Their behaviour at large orders provides information about whether they define the theory uniquely (the problem of Borel summability). It suggests methods to extract numerical information from the series when the expansion parameter is not small. The articles reprinted here deal with the explicit evaluation of large-order behaviour in many quantum mechanics and field theory models. The large-order behaviour is related to barrier penetration effects for unphysical values of the expansion parameter, which can be calculated by WKB or instanton methods. The calculation of critical exponents of &fgr;4 field theory is presented as a practical application.
Modern Functional Quantum Field Theory by Herbert M Fried Pdf
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. Contents:Basic Preliminaries:Quantum Field Theory — Why and HowFunctional PreliminariesFunctional Field TheoryThe Generating Functional and the S-MatrixSchwinger/Fradkin RepresentationsQuantum Electrodynamics:Radiative Corrections of the Photon PropagatorRadiative Corrections to the Electron PropagatorA QED Symmetry-Breaking Model of Vacuum EnergyQuantum Chromodynamics:Explicit, Non-Perturbative Gauge InvarianceQCD Transverse FluctuationsQuark Binding PotentialNucleon Scattering and BindingAstrophysical Speculations:Inflation as the Precursor of Dark EnergyQuantum Tachyon Dynamics Readership: Graduate students and researchers in quantum field theory. Keywords:Functional Methods;Quantum Field Theory;Non-Perturbative QED and QCDKey Features:Contains an explicit, non-perturbative QED argument suggesting that charge renormalization is finiteContains an explicit, new, gauge-invariant formulation of QCD, including an analytic derivation of quark binding potentials, and the first analytic extraction of Nuclear Physics from fundamental QCD: a deuteron-like potential which can bind two nucleonsContains a set of QFT Conjectures and their Astrophysical Consequences
Field Theory, The Renormalization Group, And Critical Phenomena: Graphs To Computers (3rd Edition) by Daniel J Amit,Victor Martin-mayor Pdf
This volume links field theory methods and concepts from particle physics with those in critical phenomena and statistical mechanics, the development starting from the latter point of view. Rigor and lengthy proofs are trimmed by using the phenomenological framework of graphs, power counting, etc., and field theoretic methods with emphasis on renormalization group techniques. Non-perturbative methods and numerical simulations are introduced in this new edition. Abundant references to research literature complement this matter-of-fact approach. The book introduces quantum field theory to those already grounded in the concepts of statistical mechanics and advanced quantum theory, with sufficient exercises in each chapter for use as a textbook in a one-semester graduate course.The following new chapters are included:I. Real Space MethodsII. Finite Size ScalingIII. Monte Carlo Methods. Numerical Field Theory
The book presents an extended version of the lecture course on the theory of nuclear reactions that has been given by the author for some years in Kiev State University. An account is given of the nonrelativistic nuclear reaction theory. The R — matrix description of nuclear reactions is considered and the dispersion method is formulated. Mechanisms of nuclear reactions and their relationship are studied in detail. Attention is paid to nuclear reactions involving the compound nuclear formation and to direct nuclear processes. The optical model, the diffraction approach and high — energy diffraction nuclear processes involving composite particles are discussed. It also deals with some problems treated only in special journal papers.
Advanced Quantum Theory and Its Applications Through Feynman Diagrams by Michael D. Scadron Pdf
The fundamental goal of physics is an understanding of the forces of nature in their simplest and most general terms. Yet the scientific method inadver tently steers us away from that course by requiring an ever finer subdivision of the problem into constituent components, so that the overall objective is often obscured, even to the experts. The situation is most frustrating and acute for today's graduate students, who must try to absorb as much general knowledge as is possible and also try to digest only a sm all fraction of the ever increasing morass of observational data or detailed theories to write a dissertation. This book is based on the premise that to study a subject in depth is only half the battle; the remaining struggle is to put the pieces together in a broad but comprehensive manner. Accordingly, the primary purpose of this text is to cut across the barriers existing between the various fields ofmodern physics (elementary particles; nuclear, atomic, and solid state physics; gravitation) and present a unified description of the quantum nature of forces encountered in each field at the level of the second-year physics graduate student. This unification is based on one-body perturbation techniques, covariantly generalized to what are now called "Feynman diagrams," and is formulated aS,a simple (but nontriv ial) extension of ordinary nonrelativistic, one-particle quantum theory.
Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks by Dmitry Pelinovsky,Diego Noja Pdf
This Special Issue focuses on recent progress in a new area of mathematical physics and applied analysis, namely, on nonlinear partial differential equations on metric graphs and branched networks. Graphs represent a system of edges connected at one or more branching points (vertices). The connection rule determines the graph topology. When the edges can be assigned a length and the wave functions on the edges are defined in metric spaces, the graph is called a metric graph. Evolution equations on metric graphs have attracted much attention as effective tools for the modeling of particle and wave dynamics in branched structures and networks. Since branched structures and networks appear in different areas of contemporary physics with many applications in electronics, biology, material science, and nanotechnology, the development of effective modeling tools is important for the many practical problems arising in these areas. The list of important problems includes searches for standing waves, exploring of their properties (e.g., stability and asymptotic behavior), and scattering dynamics. This Special Issue is a representative sample of the works devoted to the solutions of these and other problems.
Graphs and Patterns in Mathematics and Theoretical Physics by Mikhail Lyubich,Leon Armenovich Takhtadzhi︠a︡n,Dennis Sullivan Pdf
The Stony Brook Conference, "Graphs and Patterns in Mathematics and Theoretical Physics", was dedicated to Dennis Sullivan in honor of his sixtieth birthday. The event's scientific content, which was suggested by Sullivan, was largely based on mini-courses and survey lectures. The main idea was to help researchers and graduate students in mathematics and theoretical physics who encounter graphs in their research to overcome conceptual barriers. The collection begins with Sullivan's paper, "Sigma models and string topology," which describes a background algebraic structure for the sigma model based on algebraic topology and transversality. Other contributions to the volume were organized into five sections: Feynman Diagrams, Algebraic Structures, Manifolds: Invariants and Mirror Symmetry, Combinatorial Aspects of Dynamics, and Physics. These sections, along with more research-oriented articles, contain the following surveys: "Feynman diagrams for pedestrians and mathematicians" by M. Polyak, "Notes on universal algebra" by A. Voronov, "Unimodal maps and hierarchical models" by M. Yampolsky, and "Quantum geometry in action: big bang and black holes" by A. Ashtekar. This comprehensive volume is suitable for graduate students and research mathematicians interested in graph theory and its applications in mathematics and physics.
Adventures In Theoretical Physics: Selected Papers With Commentaries by Stephen L Adler Pdf
During the period 1964-1972, Stephen L Adler wrote seminal papers on high energy neutrino processes, current algebras, soft pion theorems, sum rules, and perturbation theory anomalies that helped lay the foundations for our current standard model of elementary particle physics. These papers are reprinted here together with detailed historical commentaries describing how they evolved, their relation to other work in the field, and their connection to recent literature. Later important work by Dr Adler on a wide range of topics in fundamental theory, phenomenology, and numerical methods, and their related historical background, is also covered in the commentaries and reprints.This book will be a valuable resource for graduate students and researchers in the fields in which Dr Adler has worked, and for historians of science studying physics in the final third of the twentieth century, a period in which an enduring synthesis was achieved.
Superstring theory is a promising theory which can potentially unify all the forces and the matters in particle physics. A new multi-dimensional object which is called "D-brane" was found. It drastically changed our perspective of a unified world. We may live on membrane-like hypersurfaces in higher dimensions ("braneworld scenario"), or we can create blackholes at particle accelarators, or the dynamics of quarks is shown to be equivalent to the higher dimensional gravity theory. All these scenarios are explained in this book with plain words but with little use of equations and with many figures. The book starts with a summary of long-standing problems in elementary particle physics and explains the D-branes and many applications of them. It ends with future roads for a unified ultimate theory of our world.
Handbook of Graph Theory by Jonathan L. Gross,Jay Yellen Pdf
The Handbook of Graph Theory is the most comprehensive single-source guide to graph theory ever published. Best-selling authors Jonathan Gross and Jay Yellen assembled an outstanding team of experts to contribute overviews of more than 50 of the most significant topics in graph theory-including those related to algorithmic and optimization approach
The Large N Expansion In Quantum Field Theory And Statistical Physics by Edouard Brezin,Spenta R Wadia Pdf
This book contains an edited comprehensive collection of reprints on the subject of the large N limit as applied to a wide spectrum of problems in quantum field theory and statistical mechanics. The topics include (1) Spin Systems; (2) Large N Limit of Gauge Theories; (3) Two-Dimensional QCD; (4) Exact Results on Planar Perturbation Series and the Nature of the 1/N Series; (5) Schwinger-Dyson Equations Approach; (6) QCD Phenomenological Lagrangians and the Large N Limit; (7) Other Approaches to Large N: Eguchi-Kawai Model, Collective Fields and Numerical Methods; (8) Matrix Models; (9) Two-Dimensional Gravity and String Theory.
Graph Theoretical Approaches to Chemical Reactivity by Danail D. Bonchev,O.G. Mekenyan Pdf
The progress in computer technology during the last 10-15 years has enabled the performance of ever more precise quantum mechanical calculations related to structure and interactions of chemical compounds. However, the qualitative models relating electronic structure to molecular geometry have not progressed at the same pace. There is a continuing need in chemistry for simple concepts and qualitatively clear pictures that are also quantitatively comparable to ab initio quantum chemical calculations. Topological methods and, more specifically, graph theory as a fixed-point topology, provide in principle a chance to fill this gap. With its more than 100 years of applications to chemistry, graph theory has proven to be of vital importance as the most natural language of chemistry. The explosive development of chemical graph theory during the last 20 years has increasingly overlapped with quantum chemistry. Besides contributing to the solution of various problems in theoretical chemistry, this development indicates that topology is an underlying principle that explains the success of quantum mechanics and goes beyond it, thus promising to bear more fruit in the future.
Santa Fe Tasi-87, The - Proceedings Of The 1987 Theoretical Advanced Study Institute In Elementary Particle Physics (In 2 Volumes) by West Geoffrey,Slansky Richard Pdf
This proceedings presents lectures on the standard model of electroweak and strong interactions, string theory, experiments and accelerators, supersymmetry and supersymmetric unified models, and the interface of astrophysics and particle physics.
