N2 Supersymmetric Dynamics For Pedestrians

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N=2 Supersymmetric Dynamics for Pedestrians

Author : Yuji Tachikawa
Publisher : Springer
ISBN 13 : 331908822X
Total Pages : 224 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis N=2 Supersymmetric Dynamics for Pedestrians by : Yuji Tachikawa

Download or read book N=2 Supersymmetric Dynamics for Pedestrians written by Yuji Tachikawa and published by Springer. This book was released on 2014-10-15 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding the dynamics of gauge theories is crucial, given the fact that all known interactions are based on the principle of local gauge symmetry. Beyond the perturbative regime, however, this is a notoriously difficult problem. Requiring invariance under supersymmetry turns out to be a suitable tool for analyzing supersymmetric gauge theories over a larger region of the space of parameters. Supersymmetric quantum field theories in four dimensions with extended N=2 supersymmetry are further constrained and have therefore been a fertile field of research in theoretical physics for quite some time. Moreover, there are far-reaching mathematical ramifications that have led to a successful dialogue with differential and algebraic geometry. These lecture notes aim to introduce students of modern theoretical physics to the fascinating developments in the understanding of N=2 supersymmetric gauge theories in a coherent fashion. Starting with a gentle introduction to electric-magnetic duality, the author guides readers through the key milestones in the field, which include the work of Seiberg and Witten, Nekrasov, Gaiotto and many others. As an advanced graduate level text, it assumes that readers have a working knowledge of supersymmetry including the formalism of superfields, as well as of quantum field theory techniques such as regularization, renormalization and anomalies. After his graduation from the University of Tokyo, Yuji Tachikawa worked at the Institute for Advanced Study, Princeton and the Kavli Institute for Physics and Mathematics of the Universe. Presently at the Department of Physics, University of Tokyo, Tachikawa is the author of several important papers in supersymmetric quantum field theories and string theory.

New Dualities of Supersymmetric Gauge Theories

Author : Jörg Teschner
Publisher : Springer
ISBN 13 : 3319187694
Total Pages : 467 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis New Dualities of Supersymmetric Gauge Theories by : Jörg Teschner

Download or read book New Dualities of Supersymmetric Gauge Theories written by Jörg Teschner and published by Springer. This book was released on 2015-11-17 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews a number of spectacular advances that have been made in the study of supersymmetric quantum field theories in the last few years. Highlights include exact calculations of Wilson loop expectation values, and highly nontrivial quantitative checks of the long-standing electric-magnetic duality conjectures The book starts with an introductory article presenting a survey of recent advances, aimed at a wide audience with a background and interest in theoretical physics. The following articles are written for advanced students and researchers in quantum field theory, string theory and mathematical physics, our goal being to familiarize these readers with the forefront of current research. The topics covered include recent advances in the classification and vacuum structure of large families of N=2 supersymmetric field theories, followed by an extensive discussion of the localisation method, one of the most powerful tools for exact studies of supersymmetric field theories. The quantities that have been studied in this way are partition functions, expectation values of line operators, and supersymmetric indices. The book also reviews recently discovered connections between SUSY field theories in four dimensions and two-dimensional conformal field theory. These connections have a counterpart in relations between three-dimensional gauge theories and Chern-Simons theory; the book’s closing chapters explore connections with string theory.

An Introduction to Two-Dimensional Quantum Field Theory with (0,2) Supersymmetry

Author : Ilarion V. Melnikov
Publisher : Springer
ISBN 13 : 3030050858
Total Pages : 482 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis An Introduction to Two-Dimensional Quantum Field Theory with (0,2) Supersymmetry by : Ilarion V. Melnikov

Download or read book An Introduction to Two-Dimensional Quantum Field Theory with (0,2) Supersymmetry written by Ilarion V. Melnikov and published by Springer. This book was released on 2019-02-11 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces two-dimensional supersymmetric field theories with emphasis on both linear and non-linear sigma models. Complex differential geometry, in connection with supersymmetry, has played a key role in most developments of the last thirty years in quantum field theory and string theory. Both structures introduce a great deal of rigidity compared to the more general categories of non-supersymmetric theories and real differential geometry, allowing for many general conceptual results and detailed quantitative predictions. Two-dimensional (0,2) supersymmetric quantum field theories provide a natural arena for the fruitful interplay between geometry and quantum field theory. These theories play an important role in string theory and provide generalizations, still to be explored fully, of rich structures such as mirror symmetry. They also have applications to non-perturbative four-dimensional physics, for instance as descriptions of surface defects or low energy dynamics of solitonic strings in four-dimensional supersymmetric theories. The purpose of these lecture notes is to acquaint the reader with these fascinating theories, assuming a background in conformal theory, quantum field theory and differential geometry at the beginning graduate level. In order to investigate the profound relations between structures from complex geometry and field theory the text begins with a thorough examination of the basic structures of (0,2) quantum field theory and conformal field theory. Next, a simple class of Lagrangian theories, the (0,2) Landau-Ginzburg models, are discussed, together with the resulting renormalization group flows, dynamics, and symmetries. After a thorough introduction and examination of (0,2) non-linear sigma models, the text introduces linear sigma models that, in particular, provide a unified treatment of non-linear sigma models and Landau-Ginzburg theories. Many exercises, along with discussions of relevant mathematical notions and important open problems in the field, are included in the text.

Instanton Counting, Quantum Geometry and Algebra

Author : Taro Kimura
Publisher : Springer Nature
ISBN 13 : 3030761908
Total Pages : 297 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Instanton Counting, Quantum Geometry and Algebra by : Taro Kimura

Download or read book Instanton Counting, Quantum Geometry and Algebra written by Taro Kimura and published by Springer Nature. This book was released on 2021-07-05 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book pedagogically describes recent developments in gauge theory, in particular four-dimensional N = 2 supersymmetric gauge theory, in relation to various fields in mathematics, including algebraic geometry, geometric representation theory, vertex operator algebras. The key concept is the instanton, which is a solution to the anti-self-dual Yang–Mills equation in four dimensions. In the first part of the book, starting with the systematic description of the instanton, how to integrate out the instanton moduli space is explained together with the equivariant localization formula. It is then illustrated that this formalism is generalized to various situations, including quiver and fractional quiver gauge theory, supergroup gauge theory. The second part of the book is devoted to the algebraic geometric description of supersymmetric gauge theory, known as the Seiberg–Witten theory, together with string/M-theory point of view. Based on its relation to integrable systems, how to quantize such a geometric structure via the Ω-deformation of gauge theory is addressed. The third part of the book focuses on the quantum algebraic structure of supersymmetric gauge theory. After introducing the free field realization of gauge theory, the underlying infinite dimensional algebraic structure is discussed with emphasis on the connection with representation theory of quiver, which leads to the notion of quiver W-algebra. It is then clarified that such a gauge theory construction of the algebra naturally gives rise to further affinization and elliptic deformation of W-algebra.

Six-Dimensional Superconformal Field Theories and Their Torus Compactifications

Author : Kantaro Ohmori
Publisher : Springer
ISBN 13 : 9811330921
Total Pages : 115 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Six-Dimensional Superconformal Field Theories and Their Torus Compactifications by : Kantaro Ohmori

Download or read book Six-Dimensional Superconformal Field Theories and Their Torus Compactifications written by Kantaro Ohmori and published by Springer. This book was released on 2018-11-03 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis describes the structures of six-dimensional (6d) superconformal field theories and its torus compactifications. The first half summarizes various aspects of 6d field theories, while the latter half investigates torus compactifications of these theories, and relates them to four-dimensional superconformal field theories in the class, called class S. It is known that compactifications of 6d conformal field theories with maximal supersymmetries provide numerous insights into four-dimensional superconformal field theories. This thesis generalizes the story to the theories with smaller supersymmetry, constructing those six-dimensional theories as brane configurations in the M-theory, and highlighting the importance of fractionalization of M5-branes. This result establishes new dualities between the theories with eight supercharges.

Space – Time – Matter

Author : Jochen Brüning
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110452154
Total Pages : 517 pages
Book Rating : 4.1/5 (14 download)

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Book Synopsis Space – Time – Matter by : Jochen Brüning

Download or read book Space – Time – Matter written by Jochen Brüning and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-04-09 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space – Time – Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail. Contents Introduction Algebraic K-theory, assembly maps, controlled algebra, and trace methods Lorentzian manifolds with special holonomy – Constructions and global properties Contributions to the spectral geometry of locally homogeneous spaces On conformally covariant differential operators and spectral theory of the holographic Laplacian Moduli and deformations Vector bundles in algebraic geometry and mathematical physics Dyson–Schwinger equations: Fix-point equations for quantum fields Hidden structure in the form factors ofN = 4 SYM On regulating the AdS superstring Constraints on CFT observables from the bootstrap program Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Yangian symmetry in maximally supersymmetric Yang-Mills theory Wave and Dirac equations on manifolds Geometric analysis on singular spaces Singularities and long-time behavior in nonlinear evolution equations and general relativity

History of Original Ideas and Basic Discoveries in Particle Physics

Author : Harvey B. Newman
Publisher : Springer Science & Business Media
ISBN 13 : 1461311470
Total Pages : 986 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis History of Original Ideas and Basic Discoveries in Particle Physics by : Harvey B. Newman

Download or read book History of Original Ideas and Basic Discoveries in Particle Physics written by Harvey B. Newman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 986 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Conference on the History of Original Ideas and Basic Discoveries, held at the "Ettore Majorana" Centre for Scientific Culture in Erice, Sicily, July 27-August 4, 1994, brought together sixty of the leading scientists including many Nobel Laureates in high energy physics, principal contributors in other fields of physics such as high Tc superconductivity, particle accelerators and detector instrumentation, and thirty-six talented younger physicists selected from candidates throughout the world. The scientific program, including 49 lectures and a discussion session on the "Status and Future Directions in High Energy Physics" was inspired by the conference theme: The key experimental discoveries and theoretical breakthroughs of the last 50 years, in particle physics and related fields, have led us to a powerful description of matter in terms of three quark and three lepton families and four fundamental interactions. The most recent generation of experiments at e+e- and proton-proton colliders, and corresponding advances in theoretical calculations, have given us remarkably precise determinations of the basic parameters of the electroweak and strong interactions. These developments, while showing the striking internal consistency of the Standard Model, have also sharpened our view of the many unanswered questions which remain for the next generation: the origin and pattern of particle masses and families, the unification of the interactions including gravity, and the relation between the laws of physics and the initial conditions of the universe.

Quantum Leap

Author :
Publisher :
ISBN 13 : 9814470619
Total Pages : pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Quantum Leap by :

Download or read book Quantum Leap written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction To Supersymmetry (2nd Edition)

Author : Muller-kirsten Harald J W
Publisher : World Scientific Publishing Company
ISBN 13 : 9813100966
Total Pages : 452 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Introduction To Supersymmetry (2nd Edition) by : Muller-kirsten Harald J W

Download or read book Introduction To Supersymmetry (2nd Edition) written by Muller-kirsten Harald J W and published by World Scientific Publishing Company. This book was released on 2010-01-21 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Supersymmetry is a symmetry which combines bosons and fermions in the same multiplet of a larger group which unites the transformations of this symmetry with that of spacetime. Thus every bosonic particle must have a fermionic partner and vice versa. Since this is not what is observed, this symmetry with inherent theoretical advantages must be badly broken. It is hoped that the envisaged collider experiments at CERN will permit a first experimental test, which is expected to revive the interest in supersymmetry considerably.This revised edition of the highly successful text of 20 years ago provides an introduction to supersymmetry, and thus begins with a substantial chapter on spacetime symmetries and spinors. Following this, graded algebras are introduced, and thereafter the supersymmetric extension of the spacetime Poincaré algebra and its representations. The Wess-Zumino model, superfields, supersymmetric Lagrangians, and supersymmetric gauge theories are treated in detail in subsequent chapters. Finally the breaking of supersymmetry is addressed meticulously. All calculations are presented in detail so that the reader can follow every step.

Strings and Geometry

Author : Clay Mathematics Institute. Summer School
Publisher : American Mathematical Soc.
ISBN 13 : 9780821837153
Total Pages : 396 pages
Book Rating : 4.8/5 (371 download)

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Book Synopsis Strings and Geometry by : Clay Mathematics Institute. Summer School

Download or read book Strings and Geometry written by Clay Mathematics Institute. Summer School and published by American Mathematical Soc.. This book was released on 2004 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains selection of expository and research article by lecturers at the school. Highlights current interests of researchers working at the interface between string theory and algebraic supergravity, supersymmetry, D-branes, the McKay correspondence andFourer-Mukai transform.

Mirror Symmetry

Author : Kentaro Hori
Publisher : American Mathematical Soc.
ISBN 13 : 0821829556
Total Pages : 954 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Mirror Symmetry by : Kentaro Hori

Download or read book Mirror Symmetry written by Kentaro Hori and published by American Mathematical Soc.. This book was released on 2003 with total page 954 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thorough and detailed exposition is the result of an intensive month-long course on mirror symmetry sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives with the aim of furthering interaction between the two fields. The material will be particularly useful for mathematicians and physicists who wish to advance their understanding across both disciplines. Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has significant mathematical consequences, the most familiar of which involves the enumeration of holomorphic curves inside complex manifolds by solving differential equations obtained from a ``mirror'' geometry. The inclusion of D-brane states in the equivalence has led to further conjectures involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds: the Gopakumar-Vafa invariants. This book gives a single, cohesive treatment of mirror symmetry. Parts 1 and 2 develop the necessary mathematical and physical background from ``scratch''. The treatment is focused, developing only the material most necessary for the task. In Parts 3 and 4 the physical and mathematical proofs of mirror symmetry are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory can be described geometrically, and thus mirror symmetry gives rise to a ``pairing'' of geometries. The proof involves applying $R\leftrightarrow 1/R$ circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Gromov-Witten theory in the algebraic setting, beginning with the moduli spaces of curves and maps, and uses localization techniques to show that certain hypergeometric functions encode the Gromov-Witten invariants in genus zero, as is predicted by mirror symmetry. Part 5 is devoted to advanced topi This one-of-a-kind book is suitable for graduate students and research mathematicians interested in mathematics and mathematical and theoretical physics.

Supersymmetry

Author : Vladimir K. Dobrev
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110527499
Total Pages : 226 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Supersymmetry by : Vladimir K. Dobrev

Download or read book Supersymmetry written by Vladimir K. Dobrev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-09-24 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: With applications in quantum field theory, general relativity and elementary particle physics, this four-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This third volume covers supersymmetry, including detailed coverage of conformal supersymmetry in four and some higher dimensions, furthermore quantum superalgebras are also considered. Contents Lie superalgebras Conformal supersymmetry in 4D Examples of conformal supersymmetry for D > 4 Quantum superalgebras

Exact Renormalization Group, The - Proceedings Of The Workshop

Author : Alexander Krasnitz
Publisher : World Scientific
ISBN 13 : 9814543578
Total Pages : 238 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Exact Renormalization Group, The - Proceedings Of The Workshop by : Alexander Krasnitz

Download or read book Exact Renormalization Group, The - Proceedings Of The Workshop written by Alexander Krasnitz and published by World Scientific. This book was released on 1999-08-13 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Quantum Field Theory in a Nutshell

Author : A. Zee
Publisher : Princeton University Press
ISBN 13 : 1400835321
Total Pages : 608 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Quantum Field Theory in a Nutshell by : A. Zee

Download or read book Quantum Field Theory in a Nutshell written by A. Zee and published by Princeton University Press. This book was released on 2010-02-01 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fully updated edition of the classic text by acclaimed physicist A. Zee Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. This expanded edition features several additional chapters, as well as an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading. The most accessible and comprehensive introductory textbook available Features a fully revised, updated, and expanded text Covers the latest exciting advances in the field Includes new exercises Offers a one-of-a-kind resource for students and researchers Leading universities that have adopted this book include: Arizona State University Boston University Brandeis University Brown University California Institute of Technology Carnegie Mellon College of William & Mary Cornell Harvard University Massachusetts Institute of Technology Northwestern University Ohio State University Princeton University Purdue University - Main Campus Rensselaer Polytechnic Institute Rutgers University - New Brunswick Stanford University University of California - Berkeley University of Central Florida University of Chicago University of Michigan University of Montreal University of Notre Dame Vanderbilt University Virginia Tech University

Perspectives on Supersymmetry II

Author : G. L. Kane
Publisher : World Scientific
ISBN 13 : 9814307505
Total Pages : 604 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Perspectives on Supersymmetry II by : G. L. Kane

Download or read book Perspectives on Supersymmetry II written by G. L. Kane and published by World Scientific. This book was released on 2010 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: Supersymmetry is at an exciting stage of development. It extends the Standard Model of particle physics into a more powerful theory that both explains more and allows more questions to be addressed. Most importantly, it opens a window for studying and testing fundamental theories at the Planck scale. Experimentally we are finally entering the intensity and energy and sensitivity regions where superpartners and supersymmetric dark matter candidates are likely to be detected, and then studied. There has been progress in understanding the remarkable physics implications of supersymmetry, including the derivation of the Higgs mechanism, the unification of the Standard Model forces, cosmological connections such as a candidate for the cold dark matter of the universe and consequences for understanding the cosmological history of the universe, and more. This volume begins with an excellent pedagogical introduction to the physics and methods and formalism of supersymmetry which is accessible to anyone with a basic knowledge of the Standard Model of particle physics.Next is an overview of open questions, followed by chapters on topics such as how to detect superpartners and tools for studying them, the current limits on superpartner masses as we enter the LHC era, the lightest superpartner as a dark matter candidate in thermal and non-thermal cosmological histories, and associated Z'' physics. Most chapters have been extended and updated from the earlier edition and some are new. This superb book will allow interested physicists to understand the coming experimental and theoretical progress in supersymmetry and the implications of discoveries of superpartners, and will also help students and workers to quickly learn new aspects of supersymmetry they want to pursue.

An Introduction To Quantum Field Theory

Author : Michael E. Peskin
Publisher : CRC Press
ISBN 13 : 0429983182
Total Pages : 866 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis An Introduction To Quantum Field Theory by : Michael E. Peskin

Download or read book An Introduction To Quantum Field Theory written by Michael E. Peskin and published by CRC Press. This book was released on 2018-05-04 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories.

Symmetries in Atomic Nuclei

Author : Alejandro Frank
Publisher : Springer Science & Business Media
ISBN 13 : 038787495X
Total Pages : 194 pages
Book Rating : 4.3/5 (878 download)

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Book Synopsis Symmetries in Atomic Nuclei by : Alejandro Frank

Download or read book Symmetries in Atomic Nuclei written by Alejandro Frank and published by Springer Science & Business Media. This book was released on 2008-12-17 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetries in Atomic Nuclei aims to present an overview of recent applications of symmetry to the description of atomic nuclei. Special care is given to a pedagogical introduction of symmetry concepts using simple examples. After a historical overview of the applications of symmetry in nuclear physics, progress in the field during the last decade is reviewed. Special emphasis is put on the introduction of neutron-proton and boson-fermion degrees of freedom. Their combination leads to a supersymmetric description of pairs and quartets of nuclei. Both theoretical aspects and experimental signatures of dynamical (super)symmetries are carefully discussed. Case studies show how these symmetries are displayed by real atomic nuclei which have been studied experimentally using state-of-the art spectroscopy. This book focuses on nuclear structure physics and has been written by active investigators in the field, but its scope is wider and is intended for final-year or post-graduate students and researchers interested in understanding the power and beauty of symmetry methods in physics.