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Author: I. T. Todorov Publisher: Elsevier ISBN: 148315632X Category : Science Languages : en Pages : 169
Book Description
Analytic Properties of Feynman Diagrams in Quantum Field Theory deals with quantum field theory, particularly in the study of the analytic properties of Feynman graphs. This book is an elementary presentation of a self-contained exposition of the majorization method used in the study of these graphs. The author has taken the intermediate position between Eden et al. who assumes the physics of the analytic properties of the S-matrix, containing physical ideas and test results without using the proper mathematical methods, and Hwa and Teplitz, whose works are more mathematically inclined with applications of algebraic topology and homology theory. The book starts with the definition of the quadratic form of a Feynman diagram, and then explains the majorization of Feynman diagrams. The book describes the derivation of spectral representations, the dispersion relations for the nucleon-nucleon scattering amplitude, and for the corresponding partial wave amplitude. The text then analyzes the surface of singularities of a Feynman diagram with notes explaining the Cutkosky rules of the Mandelstam representation for the box diagram. This text is ideal for mathematicians, physicists dealing with quantum theory and mechanics, students, and professors in advanced mathematics.
Author: I. T. Todorov Publisher: Elsevier ISBN: 148315632X Category : Science Languages : en Pages : 169
Book Description
Analytic Properties of Feynman Diagrams in Quantum Field Theory deals with quantum field theory, particularly in the study of the analytic properties of Feynman graphs. This book is an elementary presentation of a self-contained exposition of the majorization method used in the study of these graphs. The author has taken the intermediate position between Eden et al. who assumes the physics of the analytic properties of the S-matrix, containing physical ideas and test results without using the proper mathematical methods, and Hwa and Teplitz, whose works are more mathematically inclined with applications of algebraic topology and homology theory. The book starts with the definition of the quadratic form of a Feynman diagram, and then explains the majorization of Feynman diagrams. The book describes the derivation of spectral representations, the dispersion relations for the nucleon-nucleon scattering amplitude, and for the corresponding partial wave amplitude. The text then analyzes the surface of singularities of a Feynman diagram with notes explaining the Cutkosky rules of the Mandelstam representation for the box diagram. This text is ideal for mathematicians, physicists dealing with quantum theory and mechanics, students, and professors in advanced mathematics.
Author: Ivan T. Todorov Publisher: ISBN: 9780080165448 Category : Dispersion relations Languages : en Pages : 0
Book Description
Analytic Properties of Feynman Diagrams in Quantum Field Theory deals with quantum field theory, particularly in the study of the analytic properties of Feynman graphs. This book is an elementary presentation of a self-contained exposition of the majorization method used in the study of these graphs. The author has taken the intermediate position between Eden et al. who assumes the physics of the analytic properties of the S-matrix, containing physical ideas and test results without using the proper mathematical methods, and Hwa and Teplitz, whose works are more mathematically inclined with a.
Author: Eugene R. Speer Publisher: Princeton University Press ISBN: 9780691080666 Category : Mathematics Languages : en Pages : 136
Book Description
This book contains a valuable discussion of renormalization through the addition of counterterms to the Lagrangian, giving the first complete proof of the cancellation of all divergences in an arbitrary interaction. The author also introduces a new method of renormalizing an arbitrary Feynman amplitude, a method that is simpler than previous approaches and can be used to study the renormalized perturbation series in quantum field theory.
Author: Hagen Kleinert Publisher: World Scientific ISBN: 9789810246594 Category : Science Languages : en Pages : 526
Book Description
This book explains in detail how to perform perturbation expansions in quantum field theory to high orders, and how to extract the critical properties of the theory from the resulting divergent power series. These properties are calculated for various second-order phase transitions of three-dimensional systems with high accuracy, in particular the critical exponents observable in experiments close to the phase transition.Beginning with an introduction to critical phenomena, this book develops the functional-integral description of quantum field theories, their perturbation expansions, and a method for finding recursively all Feynman diagrams to any order in the coupling strength. Algebraic computer programs are supplied on accompanying World Wide Web pages. The diagrams correspond to integrals in momentum space. They are evaluated in 4-î dimensions, where they possess pole terms in 1/î. The pole terms are collected into renormalization constants.The theory of the renormalization group is used to find the critical scaling laws. They contain critical exponents which are obtained from the renormalization constants in the form of power series. These are divergent, due to factorially growing expansion coefficients. The evaluation requires resummation procedures, which are performed in two ways: (1) using traditional methods based on Pad and Borel transformations, combined with analytic mappings; (2) using modern variational perturbation theory, where the results follow from a simple strong-coupling formula. As a crucial test of the accuracy of the methods, the critical exponent à governing the divergence of the specific heat of superfluid helium is shown to agree very well with the extremely precise experimental number found in the space shuttle orbiting the earth (whose data are displayed on the cover of the book).The phi4-theories investigated in this book contain any number N of fields in an O(N)-symmetric interaction, or in an interaction in which O(N)-symmetry is broken by a term of a cubic symmetry. The crossover behavior between the different symmetries is investigated. In addition, alternative ways of obtaining critical exponents of phi4-theories are sketched, such as variational perturbation expansions in three rather than 4-î dimensions, and improved ratio tests in high-temperature expansions of lattice models.
Author: Samoil Mikhelevich Bilenʹkiĭ Publisher: Pergamon ISBN: Category : Mathematics Languages : en Pages : 206
Book Description
Introduction to Feynman Diagrams provides Feynman diagram techniques and methods for calculating quantities measured experimentally. The book discusses topics Feynman diagrams intended for experimental physicists. Topics presented include methods for calculating the matrix elements (by perturbation theory) and the basic rules for constructing Feynman diagrams; techniques for calculating cross sections and polarizations; processes in which both leptons and hadrons take part; and the electromagnetic and weak form factors of nucleons. Experimental physicists and graduate students of physics will ...
Author: I. T. Todorov
Author: I. T. Todorov
Author: Ivan T. Todorov
Author: Ivan T. Todorov
Author: I.T. Todorov
Author: 
Author: Eugene R. Speer![Critical Properties of [Greek Letter Phi]4-theories PDF](https://books.google.com/books/content/images/frontcover/rBfWk4vVi-cC?fife=w80-h100)
Author: Hagen Kleinert
Author: I. T. Todorov
Author: 
Author: Samoil Mikhelevich Bilenʹkiĭ