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Resummation and Renormalization in Effective Theories of Particle Physics

Resummation and Renormalization in Effective Theories of Particle Physics
Author: Antal Jakovác
Publisher: Springer
Total Pages: 229
Release: 2015-11-02
Genre: Science
ISBN: 3319226207

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Effective models of strong and electroweak interactions are extensively applied in particle physics phenomenology, and in many instances can compete with large-scale numerical simulations of Standard Model physics. These contexts include but are not limited to providing indications for phase transitions and the nature of elementary excitations of strong and electroweak matter. A precondition for obtaining high-precision predictions is the application of some advanced functional techniques to the effective models, where the sensitivity of the results to the accurate choice of the input parameters is under control and the insensitivity to the actual choice of ultraviolet regulators is ensured. The credibility of such attempts ultimately requires a clean renormalization procedure and an error estimation due to a necessary truncation in the resummation procedure. In this concise primer we discuss systematically and in sufficient technical depth the features of a number of approximate methods, as applied to various effective models of chiral symmetry breaking in strong interactions and the BEH-mechanism of symmetry breaking in the electroweak theory. After introducing the basics of the functional integral formulation of quantum field theories and the derivation of different variants of the equations which determine the n-point functions, the text elaborates on the formulation of the optimized perturbation theory and the large-N expansion, as applied to the solution of these underlying equations in vacuum. The optimisation aspects of the 2PI approximation is discussed. Each of them is presented as a specific reorganisation of the weak coupling perturbation theory. The dimensional reduction of high temperature field theories is discussed from the same viewpoint. The renormalization program is described for each approach in detail and particular attention is paid to the appropriate interpretation of the notion of renormalization in the presence of the Landau singularity. Finally, results which emerge from the application of these techniques to the thermodynamics of strong and electroweak interactions are reviewed in detail.


Renormalization Group and Fixed Points

Renormalization Group and Fixed Points
Author: Timothy J Hollowood
Publisher: Springer Science & Business Media
Total Pages: 78
Release: 2013-03-28
Genre: Science
ISBN: 3642363121

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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.


Principles Of Phase Structures In Particle Physics

Principles Of Phase Structures In Particle Physics
Author: Hildegard Meyer-ortmanns
Publisher: World Scientific
Total Pages: 702
Release: 2006-12-06
Genre: Science
ISBN: 9814496278

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The phase structure of particle physics shows up in matter at extremely high densities and/or temperatures as they were reached in the early universe, shortly after the big bang, or in heavy-ion collisions, as they are performed nowadays in laboratory experiments. In contrast to phase transitions of condensed matter physics, the underlying fundamental theories are better known than their macroscopic manifestations in phase transitions. These theories are quantum chromodynamics for the strong interaction part and the electroweak part of the Standard Model for the electroweak interaction. It is their non-Abelian gauge structure that makes it a big challenge to predict the type of phase conversion between phases of different symmetries and different particle contents. The book is about a variety of analytical and numerical tools that are needed to study the phase structure of particle physics. To these belong convergent and asymptotic expansions in strong and weak couplings, dimensional reduction, renormalization group studies, gap equations, Monte Carlo simulations with and without fermions, finite-size and finite-mass scaling analyses, and the approach of effective actions as supplement to first-principle calculations.


Nonperturbative Quantum Field Theory and the Structure of Matter

Nonperturbative Quantum Field Theory and the Structure of Matter
Author: T. Borne
Publisher: Springer Science & Business Media
Total Pages: 343
Release: 2005-12-19
Genre: Science
ISBN: 0306471310

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"This book, which presents a new view of quantum field theory, may serve as a research monograph and an alternative textbook examining topics which are not usually treated in conventional works." "Audience: This volume will appeal to researchers concerned with the foundation of the theory of matter and forces including gravitation. It will also be interesting to those working with quantum field theoretic methods in various disciplines, such as particle physics, nuclear physics, condensed mater physics, and relativity."--Jacket.


Gauge Theories in Particle Physics, Volume II

Gauge Theories in Particle Physics, Volume II
Author: I.J.R. Aitchison
Publisher: CRC Press
Total Pages: 484
Release: 2003-12-01
Genre: Science
ISBN: 9780849387760

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This is the second volume of the third edition of a successful text, now substantially enlarged and updated to reflect developments over the last decade in the curricula of university courses and in particle physics research. Volume I covered relativistic quantum mechanics, electromagnetism as a gauge theory, and introductory quantum field theory, and ended with the formulation and application of quantum electrodynamics (QED), including renormalization. Building on these foundations, this second volume provides a complete, accessible, and self-contained introduction to the remaining two gauge theories of the standard model of particle physics: quantum chromodynamics (QCD) and the electroweak theory. The treatment significantly extends that of the second edition in several important respects. Simple ideas of group theory are now incorporated into the discussion of non-Abelian symmetries. Two new chapters have been added on QCD, one devoted to the renormalization group and scaling violations in deep inelastic scattering and the other to non-perturbative aspects of QCD using the lattice (path-integral) formulation of quantum field theory; the latter is also used to illuminate various aspects of renormalization theory, via analogies with condensed matter systems. Three chapters treat the fundamental topic of spontaneous symmetry breaking: the (Bogoliubov) superfluid and the (BCS) superconductor are studied in some detail; one chapter is devoted to the implications of global chiral symmetry breaking in QCD; and one to the breaking of local SU(2)xU(1) symmetry in the electroweak theory. Weak interaction phenomenology is extended to include discussion of discrete symmetries and of the possibility that neutrinos are Majorana (rather than Dirac) particles. Most of these topics are normally found only in more advanced texts, and this is the first book to treat them in a manner accessible to the wide readership that the previous editions have attracted.


Emergence of Temperature in Examples and Related Nuisances in Field Theory

Emergence of Temperature in Examples and Related Nuisances in Field Theory
Author: Tamás Sándor Biró
Publisher: Springer
Total Pages: 109
Release: 2019-02-07
Genre: Science
ISBN: 3030116891

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Field theory, relying on the concept of continuous space and time while confronted with the quantum physical nature of observable quantities, still has some fundamental challenges to face. One such challenge is to understand the emergence of complexity in the behavior of interacting elementary fields, including among other things nontrivial phase structures of elementary matter at high energy density or an atypical emergence of statistical properties, e.g., when an apparent temperature is proportional to a constant acceleration in a homogeneous gravitational field. Most modern textbooks on thermal field theory are mainly concerned with how the field theory formalism should be used if a finite temperature is given. In contrast, this short primer explores how the phenomenon of temperature emerges physically for elementary fields - inquiring about the underlying kinetic field theory and the way energy fluctuations and other noise should be handled - and it investigates whether and how this harmonizes with traditional field theory concepts like spectral evolution, the Keldysh formalism, and phase transitions.


Field Theory, The Renormalization Group And Critical Phenomena (2nd Edition)

Field Theory, The Renormalization Group And Critical Phenomena (2nd Edition)
Author: Daniel J Amit
Publisher: World Scientific Publishing Company
Total Pages: 412
Release: 1984-08-31
Genre:
ISBN: 9813104147

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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. 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 Theory of Critical Phenomena

The Theory of Critical Phenomena
Author: J. J. Binney
Publisher: Oxford University Press
Total Pages: 477
Release: 1992-06-11
Genre: Science
ISBN: 0191660566

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The successful calculation of critical exponents for continuous phase transitions is one of the main achievements of theoretical physics over the last quarter-century. This was achieved through the use of scaling and field-theoretic techniques which have since become standard equipment in many areas of physics, especially quantum field theory. This book provides a thorough introduction to these techniques. Continuous phase transitions are introduced, then the necessary statistical mechanics is summarized, followed by standard models, some exact solutions and techniques for numerical simulations. The real-space renormalization group and mean-field theory are then explained and illustrated. The final chapters cover the Landau-Ginzburg model, from physical motivation, through diagrammatic perturbation theory and renormalization to the renormalization group and the calculation of critical exponents above and below the critical temperature.


Gauge Theories in Particle Physics, 40th Anniversary Edition: A Practical Introduction, Volume 2

Gauge Theories in Particle Physics, 40th Anniversary Edition: A Practical Introduction, Volume 2
Author: Ian J R Aitchison
Publisher: CRC Press
Total Pages: 1119
Release: 2024-06-19
Genre: Science
ISBN: 1040012876

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The fifth edition of this well-established, highly regarded two-volume set continues to provide a fundamental introduction to advanced particle physics while incorporating substantial new experimental results, especially in the areas of Higgs and top sector physics, as well as CP violation and neutrino oscillations. It offers an accessible and practical introduction to the three gauge theories comprising the Standard Model of particle physics: quantum electrodynamics (QED), quantum chromodynamics (QCD), and the Glashow-Salam-Weinberg (GSW) electroweak theory. Volume 2 of this updated edition covers the two non-Abelian gauge theories of QCD and the GSW theory. A distinctive feature is the extended treatment of two crucial theoretical tools: spontaneous symmetry breaking and the renormalization group. The underlying physics of these is elucidated by parallel discussions of examples from condensed matter systems: superfluidity and superconductivity, and critical phenomena. This new edition includes updates to jet algorithms, lattice field theory, CP violation and the CKM matrix, and neutrino physics. New to the fifth edition: · Tests of the Standard Model in the Higgs and top quark sectors · The naturalness problem and responses to it going beyond the Standard Model · The Standard Model as an effective field theory Each volume should serve as a valuable handbook for students and researchers in advanced particle physics looking for an accessible introduction to the Standard Model of particle physics. Ian J.R. Aitchison is Emeritus Professor of Physics at the University of Oxford. He has previously held research positions at Brookhaven National Laboratory, Saclay, and the University of Cambridge. He was a visiting professor at the University of Rochester and the University of Washington, and a scientific associate at CERN and SLAC. Dr. Aitchison has published over 90 scientific papers mainly on hadronic physics and quantum field theory. He is the author of two books and joint editor of further two. Anthony J.G. Hey is now Honorary Senior Data Scientist at the UK’s National Laboratory at Harwell. He began his career with a doctorate in particle physics from the University of Oxford. After a career in particle physics that included a professorship at the University of Southampton and research positions at Caltech, MIT and CERN, he moved to Computer Science and founded a parallel computing research group. The group were one of the pioneers of distributed memory message-passing computers and helped establish the ‘MPI’ message passing standard. After leaving Southampton in 2001 he was director of the UK’s ‘eScience’ initiative before becoming a Vice-President in Microsoft Research. He returned to the UK in 2015 as Chief Data Scientist at the U.K.’s Rutherford Appleton Laboratory. He then founded a new ‘Scientific Machine Learning’ group to apply AI technologies to the ‘Big Scientific Data’ generated by the Diamond Synchrotron, the ISIS neutron source, and the Central Laser Facility that are located on the Harwell campus. He is the author of over 100 scientific papers on physics and computing and editor of ‘The Feynman Lectures on Computation’.