Real Spinorial Groups

Author : Sebastià Xambó-Descamps
Publisher : Springer
Page : 151 pages
File Size : 50,8 Mb
Release : 2018-11-22
Category : Mathematics
ISBN : 9783030004040

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Real Spinorial Groups by Sebastià Xambó-Descamps Pdf

This book explores the Lipschitz spinorial groups (versor, pinor, spinor and rotor groups) of a real non-degenerate orthogonal geometry (or orthogonal geometry, for short) and how they relate to the group of isometries of that geometry. After a concise mathematical introduction, it offers an axiomatic presentation of the geometric algebra of an orthogonal geometry. Once it has established the language of geometric algebra (linear grading of the algebra; geometric, exterior and interior products; involutions), it defines the spinorial groups, demonstrates their relation to the isometry groups, and illustrates their suppleness (geometric covariance) with a variety of examples. Lastly, the book provides pointers to major applications, an extensive bibliography and an alphabetic index. Combining the characteristics of a self-contained research monograph and a state-of-the-art survey, this book is a valuable foundation reference resource on applications for both undergraduate and graduate students.

Author : Pierre Ramond
Publisher : Cambridge University Press
Page : 128 pages
File Size : 49,6 Mb
Release : 2010-05-13
Category : Science
ISBN : 9781139489645

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Group Theory by Pierre Ramond Pdf

Group theory has long been an important computational tool for physicists, but, with the advent of the Standard Model, it has become a powerful conceptual tool as well. This book introduces physicists to many of the fascinating mathematical aspects of group theory, and mathematicians to its physics applications. Designed for advanced undergraduate and graduate students, this book gives a comprehensive overview of the main aspects of both finite and continuous group theory, with an emphasis on applications to fundamental physics. Finite groups are extensively discussed, highlighting their irreducible representations and invariants. Lie algebras, and to a lesser extent Kac–Moody algebras, are treated in detail, including Dynkin diagrams. Special emphasis is given to their representations and embeddings. The group theory underlying the Standard Model is discussed, along with its importance in model building. Applications of group theory to the classification of elementary particles are treated in detail.

Author : Zhong-Qi Ma,Xiao-Yan Gu
Publisher : World Scientific
Page : 480 pages
File Size : 45,8 Mb
Release : 2004
Category : Science
ISBN : 9812388338

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Problems & Solutions in Group Theory for Physicists by Zhong-Qi Ma,Xiao-Yan Gu Pdf

This book is aimed at graduate students and young researchers in physics who are studying group theory and its application to physics. It contains a short explanation of the fundamental knowledge and method, and the fundamental exercises for the method, as well as some important conclusions in group theory. This book is also suitable for some graduate students in theoretical chemistry.

Author : M. A. Akivis,B. A. Rosenfeld
Publisher : American Mathematical Soc.
Page : 334 pages
File Size : 49,5 Mb
Release : 2011-07-14
Category : Mathematics
ISBN : 9780821853559

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Elie Cartan (1869-1951) by M. A. Akivis,B. A. Rosenfeld Pdf

This book describes the life and achievements of the great French mathematician, Elie Cartan. Here readers will find detailed descriptions of Cartan's discoveries in Lie groups and algebras, associative algebras, differential equations, and differential geometry, as well of later developments stemming from his ideas. There is also a biographical sketch of Cartan's life. A monumental tribute to a towering figure in the history of mathematics, this book will appeal to mathematicians and historians alike.

Author : Arnout Jozef Ceulemans
Publisher : Springer Nature
Page : 352 pages
File Size : 41,9 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9789402422450

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Group Theory Applied to Chemistry by Arnout Jozef Ceulemans Pdf

Author : Alexey P Isaev,Valery A Rubakov
Publisher : World Scientific
Page : 615 pages
File Size : 43,7 Mb
Release : 2020-07-16
Category : Science
ISBN : 9789811217425

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Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications by Alexey P Isaev,Valery A Rubakov Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 49,9 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9789814465274

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Lectures on Advanced Mathematical Methods for Physicists by Anonim Pdf

Author : Shoon K. Kim
Publisher : Cambridge University Press
Page : 512 pages
File Size : 54,8 Mb
Release : 1999-06-24
Category : Mathematics
ISBN : 9780521640626

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Group Theoretical Methods and Applications to Molecules and Crystals by Shoon K. Kim Pdf

From the pioneering author in the field, this book is ideal for condensed matter physicists and physical chemists.

Author : Ludwik Dabrowski
Publisher : Unknown
Page : 150 pages
File Size : 49,9 Mb
Release : 1988
Category : Mathematics
ISBN : UOM:39015028420068

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Group Actions on Spinors by Ludwik Dabrowski Pdf

Author : P. Barut
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401021449

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Group Theory in Non-Linear Problems by P. Barut Pdf

This is the second volume of a series of books in various aspects of Mathematical Physics. Mathematical Physics has made great strides in recent years, and is rapidly becoming an important dis cipline in its own right. The fact that physical ideas can help create new mathematical theories, and rigorous mathematical theo rems can help to push the limits of physical theories and solve problems is generally acknowledged. We believe that continuous con tacts between mathematicians and physicists and the resulting dialogue and the cross fertilization of ideas is a good thing. This series of studies is published with this goal in mind. The present volume contains contributions which were original ly presented at the Second NATO Advanced Study Institute on Mathe matical Physics held in Istanbul in the Summer of 1972. The main theme was the application of group theoretical methods in general relativity and in particle physics. Modern group theory, in par ticular, the theory of unitary irreducibl~ infinite-dimensional representations of Lie groups is being increasingly important in the formulation and solution of dynamical problems in various bran ches of physics. There is moreover a general trend of approchement of the methods of general relativity and elementary particle physics. We hope it will be useful to present these investigations to a larger audience.

Author : Tohru Eguchi,A Arima,Noboru Nakanishi
Publisher : World Scientific
Page : 546 pages
File Size : 41,9 Mb
Release : 1995-05-11
Category : Electronic
ISBN : 9789814549905

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Group Theoretical Methods In Physics - Proceedings Of The Yamada Conference Xl And Xx International Colloquium by Tohru Eguchi,A Arima,Noboru Nakanishi Pdf

The topics discussed in this volume are: Symmetry and Foundations in Classical and Quantum Mechanics; Geometry, Topology and Quantum Field Theory; Quantum Groups and Infinite-Dimensional Lie Algebras; Algebraic Approach to Nuclear Structure; Integrable Statistical Systems and Theory of Critical Phenomena Supersymmetry; Atomic and Molecular Physics; Condensed Matter Physics; Other Applications of Group Theory to Physics.

Author : Narasimhaiengar Mukunda,Subhash Chaturvedi
Publisher : Cambridge University Press
Page : 300 pages
File Size : 47,6 Mb
Release : 2022-11-30
Category : Science
ISBN : 9781009276382

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Continuous Groups for Physicists by Narasimhaiengar Mukunda,Subhash Chaturvedi Pdf

Continuous Groups for Physicists is written for graduate students as well as researchers working in the field of theoretical physics. The text has been designed uniquely and it balances coverage of advanced and non-standard topics with an equal focus on the basic concepts for a thorough understanding. The book describes the general theory of Lie groups and Lie algebras, the passage between them, and their unitary/ Hermitian representations in the quantum mechanical setting. The four infinite classical families of compact simple Lie groups and their representations are covered in detail. Readers will benefit from the discussions on topics like spinor representations of real orthogonal groups, the Schwinger representation of a group, induced representations, systems of coherent states, real symplectic groups important in quantum mechanics, Wigner's theorem on symmetry operations in quantum mechanics, ray representations of Lie groups, and groups associated with non-relativistic and relativistic space-time.

Author : Janet E. Aisbett,Victor Percy Snaith
Publisher : American Mathematical Soc.
Page : 210 pages
File Size : 51,8 Mb
Release : 1985
Category : Homology theory
ISBN : 9780821823309

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On $K_*(Z/n)$ and $K_*(\mathbf {F}_q[t]/(t^2))$ by Janet E. Aisbett,Victor Percy Snaith Pdf

This collection of papers is unified by the theme of the calculation of the low dimensional K-groups of the integers mod n and the dual numbers over a finite field.

Author : Yvette Kosmann-Schwarzbach
Publisher : Springer Science & Business Media
Page : 207 pages
File Size : 49,5 Mb
Release : 2009-10-16
Category : Mathematics
ISBN : 9780387788661

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Groups and Symmetries by Yvette Kosmann-Schwarzbach Pdf

- Combines material from many areas of mathematics, including algebra, geometry, and analysis, so students see connections between these areas - Applies material to physics so students appreciate the applications of abstract mathematics - Assumes only linear algebra and calculus, making an advanced subject accessible to undergraduates - Includes 142 exercises, many with hints or complete solutions, so text may be used in the classroom or for self study

Author : John Conway,Neil J. A. Sloane
Publisher : Springer Science & Business Media
Page : 804 pages
File Size : 48,8 Mb
Release : 1998-12-07
Category : Mathematics
ISBN : 0387985859

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Sphere Packings, Lattices and Groups by John Conway,Neil J. A. Sloane Pdf

The third edition of this definitive and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also examine such related issues as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. There is also a description of the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analogue-to-digital conversion and data compression, n-dimensional crystallography, dual theory and superstring theory in physics. New and of special interest is a report on some recent developments in the field, and an updated and enlarged supplementary bibliography with over 800 items.