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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.

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.

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.

This book is written from the viewpoint of a deep connection 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.

This book accompanies another book by the same authors, 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.

These proceedings will contain both general reviews on particle physics, astrophysics and cosmology and detailed discussions on some specific topics. Particular emphasis is put on: (i) physics and instrumentation in solar neutrino experiments (Chlorine, SAGE, GALLEX, SNO, Borexino, Iodine); (ii) present status and prospects of underwater and Antarctic experiments (Baikal, DUMAND, AMANDA, Nestor/SADCO, NEVOD); (iii) cosmic rays and cosmic ray neutrinos (high energy muons underground, atmospheric neutrinos, supernovae neutrinos); (iv) experiments on neutrino masses and mixings; (v) searches for dark matter and double beta decay.

This volume includes general reviews of recent developments in particle physics, cosmology, solar neutrinos, selected topics in astroparticle theory, new methods and projects in underground physics (such as gallium-germanium solar neutrino detector SAGE, Underground Scintillation Telescope, and EAS array “Carpet”), dark matter and double beta decay searches.

The Sixth Moscow Quantum Gravity Seminar was a continuation of the series of seminars which has played an important role in the consolidation of the international quantum gravity community and which has greatly affected the development of the field. As well as papers presented at the conference, this proceedings volume includes the papers of invited speakers who were unable to attend the seminar itself.

The strongest part of this volume is the treatment of nonperturbative field theory with implications for baryon number violation at high energies and cosmology. Also, the volume contains some fresh results concerning anyons, lattice field theory, perturbative field theory and astrophysics.

Contents:Theory: Electroweak Baryon Number Non-Conservation in Particle Physics and Cosmology (V A Rubakov)Constraints and Model Considerations for a 17 keV Neutrino (R D Peccei)Solar Neutrinos:Measurement of the Solar υe Flux with the Homestake 37Cl Detector (K Lande)SAGE: The Soviet-American Gallium Solar Neutrino Experiment (V N Gavrin)Calorimetric Measurements of an Artificial Netrino Source Activity for the Baksan Gallium-Germanium Neutrino Telescope (I N Belousov et al)The Status of Gallex (R Wink)The Sudbury Neutrino Observatory (D Sinclair)Results from Underground Experiments: Recent Results from IBM (J LoSecco & J Learned)Analysis of Rare Signals at the Baksan Underground Scintillation Telescope (E N Alexeev)Dark Matter:Axion Searches (P Sikivie)Gamma and Neutrino Astronomy/Astrophics: Five Year Anniversary of Supernova 1987A in the Large Magellanic Cloud (D K Nadyozhin)Neutrino Physics and Core Collapse Supernovae (W Hillebrandt)Cosmic Rays Origin in Active Galactic Nuclei (V I Dokuchaev)Future Experiments: Super-Kamiokande (Y Totsuka)The Lake Baikal Neutino Project (L B Bezrukov)Towards the Third Generation of Resonant Gravitational Wave Detectors (F Ricci)Readership: Particle physicists and astrophysicists.