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Recent Studies inPerturbation Theory

Recent Studies inPerturbation Theory
Author: Dimo Uzunov
Publisher: BoD – Books on Demand
Total Pages: 202
Release: 2017-06-14
Genre: Technology & Engineering
ISBN: 953513261X

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The book contains seven chapters written by noted experts and young researchers who present their recent studies of both pure mathematical problems of perturbation theories and application of perturbation methods to the study of the important topic in physics, for example, renormalization group theory and applications to basic models in theoretical physics (Y. Takashi), the quantum gravity and its detection and measurement (F. Bulnes), atom-photon interactions (E. G. Thrapsaniotis), treatment of spectra and radiation characteristics by relativistic perturbation theory (A. V. Glushkov et al), and Green's function theory and some applications (Jing Huang). The pure mathematical issues are related to the problem of generalization of the boundary layer function method for bisingularly perturbed differential equations (K. Alymkulov and D. A. Torsunov) and to the development of new homotopy asymptotic methods and some of their applications (Baojian Hong).


Studies in Perturbation Theory

Studies in Perturbation Theory
Author: Per-Olov Löwdin
Publisher:
Total Pages:
Release: 1960*
Genre: Perturbation (Quantum dynamics)
ISBN:

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Canonical Perturbation Theories

Canonical Perturbation Theories
Author: Sylvio Ferraz-Mello
Publisher: Springer Science & Business Media
Total Pages: 350
Release: 2007-05-30
Genre: Science
ISBN: 0387389059

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The book is written mainly to advanced graduate and post-graduate students following courses in Perturbation Theory and Celestial Mechanics. It is also intended to serve as a guide in research work and is written in a very explicit way: all perturbation theories are given with details allowing its immediate application to real problems. In addition, they are followed by examples showing all steps of their application.


Perturbation Theory for Matrix Equations

Perturbation Theory for Matrix Equations
Author: M. Konstantinov
Publisher: Gulf Professional Publishing
Total Pages: 443
Release: 2003-05-20
Genre: Mathematics
ISBN: 0080538673

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The book is devoted to the perturbation analysis of matrix equations. The importance of perturbation analysis is that it gives a way to estimate the influence of measurement and/or parametric errors in mathematical models together with the rounding errors done in the computational process. The perturbation bounds may further be incorporated in accuracy estimates for the solution computed in finite arithmetic. This is necessary for the development of reliable computational methods, algorithms and software from the viewpoint of modern numerical analysis. In this book a general perturbation theory for matrix algebraic equations is presented. Local and non-local perturbation bounds are derived for general types of matrix equations as well as for the most important equations arising in linear algebra and control theory. A large number of examples, tables and figures is included in order to illustrate the perturbation techniques and bounds. Key features: • The first book in this field • Can be used by a variety of specialists • Material is self-contained • Results can be used in the development of reliable computational algorithms • A large number of examples and graphical illustrations are given • Written by prominent specialists in the field


Perturbation theory for linear operators

Perturbation theory for linear operators
Author: Tosio Kato
Publisher: Springer Science & Business Media
Total Pages: 610
Release: 2013-06-29
Genre: Mathematics
ISBN: 3662126788

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Graphs in Perturbation Theory

Graphs in Perturbation Theory
Author: Michael Borinsky
Publisher: Springer
Total Pages: 173
Release: 2018-11-04
Genre: Science
ISBN: 3030035417

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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.


Perturbation Theory

Perturbation Theory
Author: Zossima Pirogov
Publisher:
Total Pages: 0
Release: 2017-12
Genre: Perturbation (Mathematics)
ISBN: 9781536129892

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"Perturbation Theory: Advances in Research and Applications begins with a deliberation on the development of a formalism of the Exchange perturbation theory (EPT) that accounts for the general identity principle of electrons that belong to different atomic centres. The possible applications of the theory concerning scattering and collision problems are discussed, and the authors apply the TDEPT to the description of the positron scattering on a Lithium atom as an example. Next, spin fluctuations in metallic multiband systems are discussed, including how to calculate the effect of itinerant spin excitations on the electronic properties and formulate a theory of spin fluctuation-induced superconductivity. The function of spin-orbit coupling is emphasized. Following this, the authors review how, governed by chiral symmetry, the long- and intermediate-range parts of the $NN$ potential unfold order by order, proceeding up to sixth order where convergence is achieved. Perturbative and nonperturbative approaches to nuclear amplitude are discussed, including the implications for renormalization. Continuing, this book presents proof of the good convergence properties of the new expansions on mathematical models that simulate the physical polarization function for light quarks and its derivative (the Adler function), in various prescriptions of renormalization-group summation. An overview of the calculation of one-loop corrections to the baryon axial vector current in the large-Nc heavy baryon chiral perturbation theory is offered, where Nc is the number of color charges. The matrix elements of the space components of the renormalization of the baryon axial vector current between SU(6) symmetric states yield the values of the axial vector couplings"--


Perturbations

Perturbations
Author: James A. Murdock
Publisher: SIAM
Total Pages: 358
Release: 1999-01-01
Genre: Mathematics
ISBN: 9781611971095

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Perturbations: Theory and Methods gives a thorough introduction to both regular and singular perturbation methods for algebraic and differential equations. Unlike most introductory books on the subject, this one distinguishes between formal and rigorous asymptotic validity, which are commonly confused in books that treat perturbation theory as a bag of heuristic tricks with no foundation. The meaning of "uniformity" is carefully explained in a variety of contexts. All standard methods, such as rescaling, multiple scales, averaging, matching, and the WKB method are covered, and the asymptotic validity (in the rigorous sense) of each method is carefully proved. First published in 1991, this book is still useful today because it is an introduction. It combines perturbation results with those known through other methods. Sometimes a geometrical result (such as the existence of a periodic solution) is rigorously deduced from a perturbation result, and at other times a knowledge of the geometry of the solutions is used to aid in the selection of an effective perturbation method. Dr. Murdock's approach differs from other introductory texts because he attempts to present perturbation theory as a natural part of a larger whole, the mathematical theory of differential equations. He explores the meaning of the results and their connections to other ways of studying the same problems.