Valery Rubakov's Books

Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications

By: Alexey P Isaev,Valery A Rubakov

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Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications

By: Alexey P Isaev,Valery A Rubakov

This book is a sequel to the book by the same authors entitled Theory of Groups and Symmetries: Finite Groups, Lie Groups, and Lie Algebras.The presentation begins with the Dirac notation, which is illustrated by boson and fermion oscillator algebras and also Grassmann algebra. Then detailed account of finite-dimensional representations of groups SL(2, C) and SU(2) and their Lie algebras is presented. The general theory of finite-dimensional irreducible representations of simple Lie algebras based on the construction of highest weight representations is given. The classification of all finite-dimensional irreducible representations of the Lie algebras of the classical series sℓ(n, C), so(n, C) and sp(2r, C) is exposed.Finite-dimensional irreducible representations of linear groups SL(N, C) and their compact forms SU(N) are constructed on the basis of the Schur-Weyl duality. A special role here is played by the theory of representations of the symmetric group algebra C[Sr] (Schur-Frobenius theory, Okounkov-Vershik approach), based on combinatorics of Young diagrams and Young tableaux. Similar construction is given for pseudo-orthogonal groups O(p, q) and SO(p, q), including Lorentz groups O(1, N-1) and SO(1, N-1), and their Lie algebras, as well as symplectic groups Sp(p, q). The representation theory of Brauer algebra (centralizer algebra of SO(p, q) and Sp(p, q) groups in tensor representations) is discussed.Finally, the covering groups Spin(p, q) for pseudo-orthogonal groups SO↑(p, q) are studied. For this purpose, Clifford algebras in spaces Rp, q are introduced and representations of these algebras are discussed.

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615

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World Scientific

Published Date

ISBN 10

9811217424

ISBN 13

9789811217425

Theory Of Groups And Symmetries: Finite Groups, Lie Groups, And Lie Algebras

By: Alexey P Isaev,Valery A Rubakov

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Theory Of Groups And Symmetries: Finite Groups, Lie Groups, And Lie Algebras

By: Alexey P Isaev,Valery A Rubakov

The book presents the main approaches in study of algebraic structures of symmetries in models of theoretical and mathematical physics, namely groups and Lie algebras and their deformations. It covers the commonly encountered quantum groups (including Yangians). The second main goal of the book is to present a differential geometry of coset spaces that is actively used in investigations of models of quantum field theory, gravity and statistical physics. The third goal is to explain the main ideas about the theory of conformal symmetries, which is the basis of the AdS/CFT correspondence.The theory of groups and symmetries is an important part of theoretical physics. In elementary particle physics, cosmology and related fields, the key role is played by Lie groups and algebras corresponding to continuous symmetries. For example, relativistic physics is based on the Lorentz and Poincare groups, and the modern theory of elementary particles — the Standard Model — is based on gauge (local) symmetry with the gauge group SU(3) x SU(2) x U(1). This book presents constructions and results of a general nature, along with numerous concrete examples that have direct applications in modern theoretical and mathematical physics.

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475

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World Scientific

Published Date

ISBN 10

9813236876

ISBN 13

9789813236875

Introduction to the Theory of the Early Universe

Cosmological Perturbations and Inflationary Theory

By: Dmitry S. Gorbunov,Valery A. Rubakov

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Introduction to the Theory of the Early Universe

Cosmological Perturbations and Inflationary Theory

By: Dmitry S. Gorbunov,Valery A. Rubakov

This book accompanies another book by the same authors, Introduction to the Theory of the Early Universe: Hot Big Bang Theory and presents the theory of the evolution of density perturbations and relic gravity waves, theory of cosmological inflation and post-inflationary reheating. Written in a pedagogical style, the main chapters give a detailed account of the established theory, with derivation of formulas. Being self-contained, it is a useful textbook for advanced undergraduate students and graduate students. Essential materials from General Relativity, theory of Gaussian random fields and quantum field theory are collected in the appendices. The more advanced topics are approached similarly in a pedagogical way. These parts may serve as a detailed introduction to current research.

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504

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World Scientific

Published Date

ISBN 10

9814343781

ISBN 13

9789814343787

Surprising Quantum Bounces

By: Valery Nesvizhevsky,Alexei Voronin

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Surprising Quantum Bounces

By: Valery Nesvizhevsky,Alexei Voronin

This unique book demonstrates the undivided unity and infinite diversity of quantum mechanics using a single phenomenon: quantum bounces of ultra-cold particles.Various examples of such 'quantum bounces' are: gravitational quantum states of ultra-cold neutrons (the first observed quantum states of matter in a gravitational field), the neutron whispering gallery (an observed matter-wave analog of the whispering gallery effect well known in acoustics and for electromagnetic waves), and gravitational and whispering gallery states for anti-matter atoms that remain to be observed.These quantum states are an invaluable tool in the search for additional fundamental short-range forces, for exploring the gravitational interaction and quantum effects of gravity, for probing physics beyond the standard model, and for furthering studies into the foundations of quantum mechanics, quantum optics, and surface science.

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Page Count

279

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

1783265981

ISBN 13

9781783265985

Classical Theory of Gauge Fields

By: Valery Rubakov

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Classical Theory of Gauge Fields

By: Valery Rubakov

Based on a highly regarded lecture course at Moscow State University, this is a clear and systematic introduction to gauge field theory. It is unique in providing the means to master gauge field theory prior to the advanced study of quantum mechanics. Though gauge field theory is typically included in courses on quantum field theory, many of its ideas and results can be understood at the classical or semi-classical level. Accordingly, this book is organized so that its early chapters require no special knowledge of quantum mechanics. Aspects of gauge field theory relying on quantum mechanics are introduced only later and in a graduated fashion--making the text ideal for students studying gauge field theory and quantum mechanics simultaneously. The book begins with the basic concepts on which gauge field theory is built. It introduces gauge-invariant Lagrangians and describes the spectra of linear perturbations, including perturbations above nontrivial ground states. The second part focuses on the construction and interpretation of classical solutions that exist entirely due to the nonlinearity of field equations: solitons, bounces, instantons, and sphalerons. The third section considers some of the interesting effects that appear due to interactions of fermions with topological scalar and gauge fields. Mathematical digressions and numerous problems are included throughout. An appendix sketches the role of instantons as saddle points of Euclidean functional integral and related topics. Perfectly suited as an advanced undergraduate or beginning graduate text, this book is an excellent starting point for anyone seeking to understand gauge fields.

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Page Count

456

Publisher

Princeton University Press

Published Date

ISBN 10

1400825091

ISBN 13

9781400825097

Introduction To The Theory Of The Early Universe: Hot Big Bang Theory (Second Edition)

By: Valery A Rubakov,Dmitry S Gorbunov

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Introduction To The Theory Of The Early Universe: Hot Big Bang Theory (Second Edition)

By: Valery A Rubakov,Dmitry S Gorbunov

This book is written from the viewpoint that a deep connection exists between cosmology and particle physics. It presents the results and ideas on both the homogeneous and isotropic Universe at the hot stage of its evolution and in later stages. The main chapters describe in a systematic and pedagogical way established facts and concepts on the early and the present Universe. The comprehensive treatment, hence, serves as a modern introduction to this rapidly developing field of science. To help in reading the chapters without having to constantly consult other texts, essential materials from General Relativity and the theory of elementary particles are collected in the appendices. Various hypotheses dealing with unsolved problems of cosmology, and often alternative to each other, are discussed at a more advanced level. These concern dark matter, dark energy, matter-antimatter asymmetry, etc.Particle physics and cosmology underwent rapid development between the first and the second editions of this book. In the second edition, many chapters and sections have been revised, and numerical values of particle physics and cosmological parameters have been updated.

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Page Count

594

Publisher

World Scientific

Published Date

ISBN 10

9813220058

ISBN 13

9789813220058

Theory Of Groups And Symmetries: Finite Groups, Lie Groups, And Lie Algebras

By: Alexey P Isaev,Valery A Rubakov

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Theory Of Groups And Symmetries: Finite Groups, Lie Groups, And Lie Algebras

By: Alexey P Isaev,Valery A Rubakov

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Page Count

475

Publisher

World Scientific

Published Date

ISBN 10

9813236876

ISBN 13

9789813236875

Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications

By: Alexey P Isaev,Valery A Rubakov

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Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications

By: Alexey P Isaev,Valery A Rubakov

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Solve jigsaw puzzle

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Page Count

615

Publisher

World Scientific

Published Date

ISBN 10

9811217424

ISBN 13

9789811217425

Book's by Valery Rubakov

Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications

Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications

Theory Of Groups And Symmetries: Finite Groups, Lie Groups, And Lie Algebras

Theory Of Groups And Symmetries: Finite Groups, Lie Groups, And Lie Algebras

Introduction to the Theory of the Early Universe

Introduction to the Theory of the Early Universe

Surprising Quantum Bounces

Surprising Quantum Bounces

Classical Theory of Gauge Fields

Classical Theory of Gauge Fields

Introduction To The Theory Of The Early Universe: Hot Big Bang Theory (Second Edition)

Introduction To The Theory Of The Early Universe: Hot Big Bang Theory (Second Edition)

Theory Of Groups And Symmetries: Finite Groups, Lie Groups, And Lie Algebras

Theory Of Groups And Symmetries: Finite Groups, Lie Groups, And Lie Algebras

Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications

Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications

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