Analytic Properties Of Feynman Diagrams In Quantum Field Theory
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Analytic Properties Of Feynman Diagrams In Quantum Field Theory
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Author : I. T. Todorov
language : en
Publisher: Elsevier
Release Date : 2014-05-17
Analytic Properties Of Feynman Diagrams In Quantum Field Theory written by I. T. Todorov and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-17 with Science categories.
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.
Analytic Properties Of Feynman Diagrams In Quantum Field Theory Tr From The Russian
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Author :
language : en
Publisher:
Release Date : 1971
Analytic Properties Of Feynman Diagrams In Quantum Field Theory Tr From The Russian written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Dispersion relations categories.
Analytic Properties Of Feynman Diagrams In Quantum Field Theory
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Author : Ivan T. Todorov
language : en
Publisher:
Release Date : 1971
Analytic Properties Of Feynman Diagrams In Quantum Field Theory written by Ivan T. Todorov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Dispersion relations categories.
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.
Analytical Properties Of Feynman Diagrams In Quantum Field Theory
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Author : Ivan T. Todorov
language : en
Publisher:
Release Date : 1971
Analytical Properties Of Feynman Diagrams In Quantum Field Theory written by Ivan T. Todorov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematical physics categories.
Critical Properties Of Phi4 Theories
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Author : Hagen Kleinert
language : en
Publisher: World Scientific
Release Date : 2001-07-30
Critical Properties Of Phi4 Theories written by Hagen Kleinert and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-07-30 with Science categories.
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-ε dimensions, where they possess pole terms in 1/ε. 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 Padé 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 α 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-ε dimensions, and improved ratio tests in high-temperature expansions of lattice models.
Analytic Properties Of Feynham Diagrams In Quantum Field Theory
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Author : I.T. Todorov
language : en
Publisher:
Release Date : 1971
Analytic Properties Of Feynham Diagrams In Quantum Field Theory written by I.T. Todorov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with categories.
Critical Properties Of Greek Letter Phi 4 Theories
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Author : Hagen Kleinert
language : en
Publisher: World Scientific
Release Date : 2001
Critical Properties Of Greek Letter Phi 4 Theories written by Hagen Kleinert and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Science categories.
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.
Modern Functional Quantum Field Theory Summing Feynman Graphs
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Author : Herbert Martin Fried
language : en
Publisher: World Scientific
Release Date : 2014-01-10
Modern Functional Quantum Field Theory Summing Feynman Graphs written by Herbert Martin Fried and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-10 with Science categories.
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.
What Is The I For The S Matrix
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Author : Holmfridur Sigridar Hannesdottir
language : en
Publisher: Springer Nature
Release Date : 2023-01-01
What Is The I For The S Matrix written by Holmfridur Sigridar Hannesdottir and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Science categories.
This book provides a modern perspective on the analytic structure of scattering amplitudes in quantum field theory, with the goal of understanding and exploiting consequences of unitarity, causality, and locality. It focuses on the question: Can the S-matrix be complexified in a way consistent with causality? The affirmative answer has been well understood since the 1960s, in the case of 2→2 scattering of the lightest particle in theories with a mass gap at low momentum transfer, where the S-matrix is analytic everywhere except at normal-threshold branch cuts. We ask whether an analogous picture extends to realistic theories, such as the Standard Model, that include massless fields, UV/IR divergences, and unstable particles. Especially in the presence of light states running in the loops, the traditional iε prescription for approaching physical regions might break down, because causality requirements for the individual Feynman diagrams can be mutually incompatible. We demonstrate that such analyticity problems are not in contradiction with unitarity. Instead, they should be thought of as finite-width effects that disappear in the idealized 2→2 scattering amplitudes with no unstable particles, but might persist at higher multiplicity. To fix these issues, we propose an iε-like prescription for deforming branch cuts in the space of Mandelstam invariants without modifying the analytic properties of the physical amplitude. This procedure results in a complex strip around the real part of the kinematic space, where the S-matrix remains causal. We illustrate all the points on explicit examples, both symbolically and numerically, in addition to giving a pedagogical introduction to the analytic properties of the perturbative S-matrix from a modern point of view. To help with the investigation of related questions, we introduce a number of tools, including holomorphic cutting rules, new approaches to dispersion relations, as well as formulae for local behavior of Feynman integrals near branch points. This book is well suited for anyone with knowledge of quantum field theory at a graduate level who wants to become familiar with the complex-analytic structure of Feynman integrals.
Methods Of Quantum Field Theory In Statistical Physics
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Author : Alekse? Alekseevich Abrikosov
language : en
Publisher: Courier Corporation
Release Date : 1975-10-01
Methods Of Quantum Field Theory In Statistical Physics written by Alekse? Alekseevich Abrikosov and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-10-01 with Science categories.
This comprehensive introduction to the many-body theory was written by three renowned physicists and acclaimed by American Scientist as "a classic text on field theoretic methods in statistical physics."