Author: Timothy J Hollowood
Publisher: Springer Science & Business Media
ISBN: 3642363121
Category : Science
Languages : en
Pages : 70
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Book Description
This Brief presents an introduction to the theory of the renormalization group in the context of quantum field theories of relevance to particle physics. Emphasis is placed on gaining a physical understanding of the running of the couplings. The Wilsonian version of the renormalization group is related to conventional perturbative calculations with dimensional regularization and minimal subtraction. An introduction is given to some of the remarkable renormalization group properties of supersymmetric theories.
Author: John Cardy
Publisher: Cambridge University Press
ISBN: 9780521499590
Category : Science
Languages : en
Pages : 264
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Book Description
This text provides a thoroughly modern graduate-level introduction to the theory of critical behaviour. It begins with a brief review of phase transitions in simple systems, then goes on to introduce the core ideas of the renormalisation group.
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: Nigel Goldenfeld
Publisher: CRC Press
ISBN: 0429962045
Category : Science
Languages : en
Pages : 417
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Book Description
Covering the elementary aspects of the physics of phases transitions and the renormalization group, this popular book is widely used both for core graduate statistical mechanics courses as well as for more specialized courses. Emphasizing understanding and clarity rather than technical manipulation, these lectures de-mystify the subject and show precisely "how things work." Goldenfeld keeps in mind a reader who wants to understand why things are done, what the results are, and what in principle can go wrong. The book reaches both experimentalists and theorists, students and even active researchers, and assumes only a prior knowledge of statistical mechanics at the introductory graduate level.Advanced, never-before-printed topics on the applications of renormalization group far from equilibrium and to partial differential equations add to the uniqueness of this book.
Author: Jean Zinn-Justin
Publisher: Oxford University Press on Demand
ISBN: 0199227195
Category : Mathematics
Languages : en
Pages : 465
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Book Description
No further information has been provided for this title.
Author: Alexander Krasnitz
Publisher: World Scientific
ISBN: 9814543578
Category :
Languages : en
Pages : 238
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Book Description
The subject of the exact renormalization group started from pioneering work by Wegner and Houghton in the early seventies and, a decade later, by Polchinski, who formulated the Wilson renormalization group for field theory. In the past decade considerable progress has been made in this field, which includes the development of alternative formulations of the approach and of powerful techniques for solving the exact renormalization group equations, as well as widening of the scope of the exact renormalization group method to include fermions and gauge fields. In particular, two very recent results, namely the manifestly gauge-invariant formulation of the exact renormalization group equation and the proof of the c-theorem in four dimensions, are presented in this volume.
Author: Belal Ehsan Baaquie
Publisher: Cambridge University Press
ISBN: 1108502423
Category : Science
Languages : en
Pages : 717
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Book Description
An introduction to how the mathematical tools from quantum field theory can be applied to economics and finance, providing a wide range of quantum mathematical techniques for designing financial instruments. The ideas of Lagrangians, Hamiltonians, state spaces, operators and Feynman path integrals are demonstrated to be the mathematical underpinning of quantum field theory, and which are employed to formulate a comprehensive mathematical theory of asset pricing as well as of interest rates, which are validated by empirical evidence. Numerical algorithms and simulations are applied to the study of asset pricing models as well as of nonlinear interest rates. A range of economic and financial topics are shown to have quantum mechanical formulations, including options, coupon bonds, nonlinear interest rates, risky bonds and the microeconomic action functional. This is an invaluable resource for experts in quantitative finance and in mathematics who have no specialist knowledge of quantum field theory.
Author: Hidetoshi Nishimori
Publisher: Oxford University Press
ISBN: 0199577226
Category : Science
Languages : en
Pages : 373
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Book Description
As an introductory account of the theory of phase transitions and critical phenomena, this book reflects lectures given by the authors to graduate students at their departments and is thus classroom-tested to help beginners enter the field. Most parts are written as self-contained units and every new concept or calculation is explained in detail without assuming prior knowledge of the subject. The book significantly enhances and revises a Japanese version which is a bestseller in the Japanese market and is considered a standard textbook in the field. It contains new pedagogical presentations of field theory methods, including a chapter on conformal field theory, and various modern developments hard to find in a single textbook on phase transitions. Exercises are presented as the topics develop, with solutions found at the end of the book, making the text useful for self-teaching, as well as for classroom learning.
Author: D V Shirkov
Publisher: World Scientific
ISBN: 981455524X
Category :
Languages : en
Pages : 372
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Book Description
The papers included here deal with the many faces of renormalization group formalism as it is used in different branches of theoretical physics. The subjects covered emphasize various applications to the theory of turbulence, chaos, quantum chaos in dynamical systems, spin systems and vector models. Also discussed are applications to related topics such as quantum field theory and chromodynamics, high temperature superconductivity and plasma physics. Contents:RG in Chern-Simons Field Theories and High-temperature Superconductivity (L V Avdeev & D I Kazakov)The Three-Loop QED Photon Vacuum Polarization Function in the MS-Scheme and the Four-Loop QED β-Function in the On-Shell Scheme (S G Gorishny et al)Method of Effective Charges and Brodsky-Lepage-MacKenzie Criterion (G Grunberg)Critical Exponents for Ising-Like Systems in Non-Integer Dimensions from Field Theory (Yu Holovatch & M Shpot)Scaling in Superconductors: Three-loop RG Expansions for a Three-Dimensional Model with Three Coupling Constants (S A Antonenko & A I Sokolov)A Renormalization Group Analysis of Frustrated Non-Collinear Magnets (P Azaria & B Delamotte)Critical Properties of the N-Vector Model Near Large-Scale Defects (R Z Bariev && I Z Ilaldinov)Dynamics of the Inhomogeneous Excitations in the One-Dimensional Isotropic X-Y Model of Spin s=1/2 (G O Berim)The Principle of Maximal Randomness in the Theory of Fully Developed Turbulence (L Ts Adzhemyan & M Yu Nalimov)Chaotic Renormalization Group Transformations (P H Damagaard)Symmetry Breaking Bifurcations in Chaotic Systems (P Grassberger & A S Pikovsky)The Renormalization Group Method Based on Group Analysis (V F Kovalev et al)and other papers Readership: Theoretical, statistical, mathematical and nuclear physics. keywords:
Author: Gérard Toulouse
Publisher: John Wiley & Sons
ISBN:
Category : Mathematics
Languages : en
Pages : 206
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Book Description
