Group Theory General Relativity

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Group Theory and General Relativity

Moshe Carmeli
Group Theory and General Relativity Book PDF

Author : Moshe Carmeli
Publisher : World Scientific
Page : 416 pages
File Size : 51,8 Mb
Release : 2000
Category : Science
ISBN : 1860942342

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Group Theory and General Relativity by Moshe Carmeli Pdf

This is the only book on the subject of group theory and Einstein's theory of gravitation. It contains an extensive discussion on general relativity from the viewpoint of group theory and gauge fields. It also puts together in one volume many scattered, original works, on the use of group theory in general relativity theory. There are twelve chapters in the book. The first six are devoted to rotation and Lorentz groups, and their representations. They include the spinor representation as well as the infinite-dimensional representations. The other six chapters deal with the application of groups -- particularly the Lorentz and the SL(2, C) groups -- to the theory of general relativity. Each chapter is concluded with a set of problems. The topics covered range from the fundamentals of general relativity theory, its formulation as an SL(2, C) gauge theory, to exact solutions of the Einstein gravitational field equations. The important Bondi-Metzner-Sachs group, and its representations, conclude the book The entire book is self-contained in both group theory and general relativity theory, and no prior knowledge of either is assumed. The subject of this book constitutes a relevant link between field theoreticians and general relativity theoreticians, who usually work rather independently of each other. The treatise is highly topical and of real interest to theoretical physicists, general relativists and applied mathematicians. It is invaluable to graduate students and research workers in quantum field theory, general relativity and elementary particle theory.

Theory and Applications of the Poincaré Group

Young Suh Kim,M. Noz
Theory and Applications of the Poincar Group Book PDF

Author : Young Suh Kim,M. Noz
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400945586

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Theory and Applications of the Poincaré Group by Young Suh Kim,M. Noz Pdf

Special relativity and quantum mechanics, formulated early in the twentieth century, are the two most important scientific languages and are likely to remain so for many years to come. In the 1920's, when quantum mechanics was developed, the most pressing theoretical problem was how to make it consistent with special relativity. In the 1980's, this is still the most pressing problem. The only difference is that the situation is more urgent now than before, because of the significant quantity of experimental data which need to be explained in terms of both quantum mechanics and special relativity. In unifying the concepts and algorithms of quantum mechanics and special relativity, it is important to realize that the underlying scientific language for both disciplines is that of group theory. The role of group theory in quantum mechanics is well known. The same is true for special relativity. Therefore, the most effective approach to the problem of unifying these two important theories is to develop a group theory which can accommodate both special relativity and quantum mechanics. As is well known, Eugene P. Wigner is one of the pioneers in developing group theoretical approaches to relativistic quantum mechanics. His 1939 paper on the inhomogeneous Lorentz group laid the foundation for this important research line. It is generally agreed that this paper was somewhat ahead of its time in 1939, and that contemporary physicists must continue to make real efforts to appreciate fully the content of this classic work.

Group Theory in a Nutshell for Physicists

A. Zee
Group Theory in a Nutshell for Physicists Book PDF

Author : A. Zee
Publisher : Princeton University Press
Page : 632 pages
File Size : 48,6 Mb
Release : 2016-03-29
Category : Science
ISBN : 9781400881185

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Group Theory in a Nutshell for Physicists by A. Zee Pdf

A concise, modern textbook on group theory written especially for physicists Although group theory is a mathematical subject, it is indispensable to many areas of modern theoretical physics, from atomic physics to condensed matter physics, particle physics to string theory. In particular, it is essential for an understanding of the fundamental forces. Yet until now, what has been missing is a modern, accessible, and self-contained textbook on the subject written especially for physicists. Group Theory in a Nutshell for Physicists fills this gap, providing a user-friendly and classroom-tested text that focuses on those aspects of group theory physicists most need to know. From the basic intuitive notion of a group, A. Zee takes readers all the way up to how theories based on gauge groups could unify three of the four fundamental forces. He also includes a concise review of the linear algebra needed for group theory, making the book ideal for self-study. Provides physicists with a modern and accessible introduction to group theory Covers applications to various areas of physics, including field theory, particle physics, relativity, and much more Topics include finite group and character tables; real, pseudoreal, and complex representations; Weyl, Dirac, and Majorana equations; the expanding universe and group theory; grand unification; and much more The essential textbook for students and an invaluable resource for researchers Features a brief, self-contained treatment of linear algebra An online illustration package is available to professors Solutions manual (available only to professors)

Group Theory & General Relativity

Moshe Carmeli
Group Theory General Relativity Book PDF

Author : Moshe Carmeli
Publisher : World Scientific
Page : 412 pages
File Size : 49,7 Mb
Release : 2000-11-15
Category : Science
ISBN : 9781783261697

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Group Theory & General Relativity by Moshe Carmeli Pdf

This is the only book on the subject of group theory and Einstein's theory of gravitation. It contains an extensive discussion on general relativity from the viewpoint of group theory and gauge fields. It also puts together in one volume many scattered, original works, on the use of group theory in general relativity theory.There are twelve chapters in the book. The first six are devoted to rotation and Lorentz groups, and their representations. They include the spinor representation as well as the infinite-dimensional representations. The other six chapters deal with the application of groups -particularly the Lorentz and the SL(2,C) groups — to the theory of general relativity. Each chapter is concluded with a set of problems.The topics covered range from the fundamentals of general relativity theory, its formulation as an SL(2,C) gauge theory, to exact solutions of the Einstein gravitational field equations. The important Bondi-Metzner-Sachs group, and its representations, conclude the book. The entire book is self-contained in both group theory and general relativity theory, and no prior knowledge of either is assumed.The subject of this book constitutes a relevant link between field theoreticians and general relativity theoreticians, who usually work rather independently of each other. The treatise is highly topical and of real interest to theoretical physicists, general relativists and applied mathematicians. It is invaluable to graduate students and research workers in quantum field theory, general relativity and elementary particle theory.

Applications of the Theory of Groups in Mechanics and Physics

Petre P. Teodorescu,Nicolae-A.P. Nicorovici
Applications of the Theory of Groups in Mechanics and Physics Book PDF

Author : Petre P. Teodorescu,Nicolae-A.P. Nicorovici
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 40,5 Mb
Release : 2004-04-30
Category : Mathematics
ISBN : 9781402020476

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Applications of the Theory of Groups in Mechanics and Physics by Petre P. Teodorescu,Nicolae-A.P. Nicorovici Pdf

The notion of group is fundamental in our days, not only in mathematics, but also in classical mechanics, electromagnetism, theory of relativity, quantum mechanics, theory of elementary particles, etc. This notion has developed during a century and this development is connected with the names of great mathematicians as E. Galois, A. L. Cauchy, C. F. Gauss, W. R. Hamilton, C. Jordan, S. Lie, E. Cartan, H. Weyl, E. Wigner, and of many others. In mathematics, as in other sciences, the simple and fertile ideas make their way with difficulty and slowly; however, this long history would have been of a minor interest, had the notion of group remained connected only with rather restricted domains of mathematics, those in which it occurred at the beginning. But at present, groups have invaded almost all mathematical disciplines, mechanics, the largest part of physics, of chemistry, etc. We may say, without exaggeration, that this is the most important idea that occurred in mathematics since the invention of infinitesimal calculus; indeed, the notion of group expresses, in a precise and operational form, the vague and universal ideas of regularity and symmetry. The notion of group led to a profound understanding of the character of the laws which govern natural phenomena, permitting to formulate new laws, correcting certain inadequate formulations and providing unitary and non contradictory formulations for the investigated phenomena.

The Theory of Groups and Quantum Mechanics

Hermann Weyl
The Theory of Groups and Quantum Mechanics Book PDF

Author : Hermann Weyl
Publisher : Courier Corporation
Page : 468 pages
File Size : 47,9 Mb
Release : 1950-01-01
Category : Mathematics
ISBN : 0486602699

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The Theory of Groups and Quantum Mechanics by Hermann Weyl Pdf

This landmark among mathematics texts applies group theory to quantum mechanics, first covering unitary geometry, quantum theory, groups and their representations, then applications themselves — rotation, Lorentz, permutation groups, symmetric permutation groups, and the algebra of symmetric transformations.

Group Theory and General Relativity

Moshe Carmeli,AEROSPACE RESEARCH LABS WRIGHT-PATTERSON AFB OHIO.
Group Theory and General Relativity Book PDF

Author : Moshe Carmeli,AEROSPACE RESEARCH LABS WRIGHT-PATTERSON AFB OHIO.
Publisher : Unknown
Page : 199 pages
File Size : 48,7 Mb
Release : 1972
Category : Electronic
ISBN : OCLC:606167252

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Group Theory and General Relativity by Moshe Carmeli,AEROSPACE RESEARCH LABS WRIGHT-PATTERSON AFB OHIO. Pdf

The report discusses research performed in group theory and general relativity. It includes the following: Representations of the rotation group; Representations of the Lorentz group; SL(2, C) symmetry of the gravitational field; Applications of the group SU(2) to gravitational and electromagnetic fields; Equations of motion in general relativity; and Miscellaneous. (Author).

Problems in the General Theory of Relativity and Theory of Group Representations

N. G. Basov
Problems in the General Theory of Relativity and Theory of Group Representations Book PDF

Author : N. G. Basov
Publisher : Springer Science & Business Media
Page : 191 pages
File Size : 42,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781468406764

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Problems in the General Theory of Relativity and Theory of Group Representations by N. G. Basov Pdf

This collection contains survey articles dealing with the following topics: The Mach principle and its role in the general theory of relativity, the modern conception of the vacuum, new methods in the theory of Lie group representations, the coherent state method and its application to physical problems, and the Newman-Penrose method and its application to problems in general relativity theory.

Group Theory for Physicists

Pichai Ramadevi,Varun Dubey
Group Theory for Physicists Book PDF

Author : Pichai Ramadevi,Varun Dubey
Publisher : Cambridge University Press
Page : 175 pages
File Size : 43,5 Mb
Release : 2019-12-12
Category : Science
ISBN : 9781108429474

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Group Theory for Physicists by Pichai Ramadevi,Varun Dubey Pdf

Covers two important aspects of group theory namely discrete groups and Lie groups.

Group Theory in Quantum Mechanics

Volker Heine
Group Theory in Quantum Mechanics Book PDF

Author : Volker Heine
Publisher : Elsevier
Page : 479 pages
File Size : 45,6 Mb
Release : 2014-05-15
Category : Science
ISBN : 9781483152004

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Group Theory in Quantum Mechanics by Volker Heine Pdf

Group Theory in Quantum Mechanics: An Introduction to its Present Usage introduces the reader to the three main uses of group theory in quantum mechanics: to label energy levels and the corresponding eigenstates; to discuss qualitatively the splitting of energy levels as one starts from an approximate Hamiltonian and adds correction terms; and to aid in the evaluation of matrix elements of all kinds, and in particular to provide general selection rules for the non-zero ones. The theme is to show how all this is achieved by considering the symmetry properties of the Hamiltonian and the way in which these symmetries are reflected in the wave functions. This book is comprised of eight chapters and begins with an overview of the necessary mathematical concepts, including representations and vector spaces and their relevance to quantum mechanics. The uses of symmetry properties and mathematical expression of symmetry operations are also outlined, along with symmetry transformations of the Hamiltonian. The next chapter describes the three uses of group theory, with particular reference to the theory of atomic energy levels and transitions. The following chapters deal with the theory of free atoms and ions; representations of finite groups; the electronic structure and vibrations of molecules; solid state physics; and relativistic quantum mechanics. Nuclear physics is also discussed, with emphasis on the isotopic spin formalism, nuclear forces, and the reactions that arise when the nuclei take part in time-dependent processes. This monograph will be of interest to physicists and mathematicians.

Group Theory for the Standard Model of Particle Physics and Beyond

Ken J. Barnes
Group Theory for the Standard Model of Particle Physics and Beyond Book PDF

Author : Ken J. Barnes
Publisher : CRC Press
Page : 0 pages
File Size : 54,7 Mb
Release : 2010-03-10
Category : Science
ISBN : 1420078747

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Group Theory for the Standard Model of Particle Physics and Beyond by Ken J. Barnes Pdf

Based on the author’s well-established courses, Group Theory for the Standard Model of Particle Physics and Beyond explores the use of symmetries through descriptions of the techniques of Lie groups and Lie algebras. The text develops the models, theoretical framework, and mathematical tools to understand these symmetries. After linking symmetries with conservation laws, the book works through the mathematics of angular momentum and extends operators and functions of classical mechanics to quantum mechanics. It then covers the mathematical framework for special relativity and the internal symmetries of the standard model of elementary particle physics. In the chapter on Noether’s theorem, the author explains how Lagrangian formalism provides a natural framework for the quantum mechanical interpretation of symmetry principles. He then examines electromagnetic, weak, and strong interactions; spontaneous symmetry breaking; the elusive Higgs boson; and supersymmetry. He also introduces new techniques based on extending space–time into dimensions described by anticommuting coordinates. Designed for graduate and advanced undergraduate students in physics, this text provides succinct yet complete coverage of the group theory of the symmetries of the standard model of elementary particle physics. It will help students understand current knowledge about the standard model as well as the physics that potentially lies beyond the standard model.

Special Relativity and Quantum Theory

M. Noz,Young Suh Kim
Special Relativity and Quantum Theory Book PDF

Author : M. Noz,Young Suh Kim
Publisher : Springer Science & Business Media
Page : 510 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400930513

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Special Relativity and Quantum Theory by M. Noz,Young Suh Kim Pdf

Special relativity and quantum mechanics are likely to remain the two most important languages in physics for many years to come. The underlying language for both disciplines is group theory. Eugene P. Wigner's 1939 paper on the Unitary Representations of the Inhomogeneous Lorentz Group laid the foundation for unifying the concepts and algorithms of quantum mechanics and special relativity. In view of the strong current interest in the space-time symmetries of elementary particles, it is safe to say that Wigner's 1939 paper was fifty years ahead of its time. This edited volume consists of Wigner's 1939 paper and the major papers on the Lorentz group published since 1939. . This volume is intended for graduate and advanced undergraduate students in physics and mathematics, as well as mature physicists wishing to understand the more fundamental aspects of physics than are available from the fashion-oriented theoretical models which come and go. The original papers contained in this volume are useful as supplementary reading material for students in courses on group theory, relativistic quantum mechanics and quantum field theory, relativistic electrodynamics, general relativity, and elementary particle physics. This reprint collection is an extension of the textbook by the present editors entitled "Theory and Applications of the Poincare Group." Since this book is largely based on the articles contained herein, the present volume should be viewed as a reading for the previous work. continuation of and supplementary We would like to thank Professors J. Bjorken, R. Feynman, R. Hofstadter, J.

Not Even Wrong

Peter Woit
Not Even Wrong Book PDF

Author : Peter Woit
Publisher : Random House
Page : 306 pages
File Size : 52,8 Mb
Release : 2011-08-31
Category : Science
ISBN : 9781446443019

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Not Even Wrong by Peter Woit Pdf

Not Even Wrong is a fascinating exploration of our attempts to come to grips with perhaps the most intellectually demanding puzzle of all: how does the universe work at its most fundamnetal level? The book begins with an historical survey of the experimental and theoretical developments that led to the creation of the phenomenally successful 'Standard Model' of particle physics around 1975. Despite its successes, the Standard Model does not answer all the key questions and physicists continuing search for answers led to the development of superstring theory. However, after twenty years, superstring theory has failed to advance beyond the Standard Model. The absence of experimental evidence is at the core of this controversial situation which means that it is impossible to prove that superstring theory is either right or wrong. To date, only the arguments of the theory's advocates have received much publicity. Not Even Wrong provides readers with another side of the story.

Group Theory in a Nutshell for Physicists

A. Zee
Group Theory in a Nutshell for Physicists Book PDF

Author : A. Zee
Publisher : Princeton University Press
Page : 632 pages
File Size : 50,6 Mb
Release : 2016-03-29
Category : Science
ISBN : 9780691162690

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Group Theory in a Nutshell for Physicists by A. Zee Pdf

A concise, modern textbook on group theory written especially for physicists Although group theory is a mathematical subject, it is indispensable to many areas of modern theoretical physics, from atomic physics to condensed matter physics, particle physics to string theory. In particular, it is essential for an understanding of the fundamental forces. Yet until now, what has been missing is a modern, accessible, and self-contained textbook on the subject written especially for physicists. Group Theory in a Nutshell for Physicists fills this gap, providing a user-friendly and classroom-tested text that focuses on those aspects of group theory physicists most need to know. From the basic intuitive notion of a group, A. Zee takes readers all the way up to how theories based on gauge groups could unify three of the four fundamental forces. He also includes a concise review of the linear algebra needed for group theory, making the book ideal for self-study. Provides physicists with a modern and accessible introduction to group theory Covers applications to various areas of physics, including field theory, particle physics, relativity, and much more Topics include finite group and character tables; real, pseudoreal, and complex representations; Weyl, Dirac, and Majorana equations; the expanding universe and group theory; grand unification; and much more The essential textbook for students and an invaluable resource for researchers Features a brief, self-contained treatment of linear algebra An online illustration package is available to professors Solutions manual (available only to professors)

The Special Theory of Relativity

Helmut Günther,Volker Müller
The Special Theory of Relativity Book PDF

Author : Helmut Günther,Volker Müller
Publisher : Springer Nature
Page : 542 pages
File Size : 52,5 Mb
Release : 2019-09-25
Category : Science
ISBN : 9789811377839

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The Special Theory of Relativity by Helmut Günther,Volker Müller Pdf

This book discusses in detail the special theory of relativity without including all the instruments of theoretical physics, enabling readers who are not budding theoretical physicists to develop competence in the field. An arbitrary but fixed inertial system is chosen, where the known velocity of light is measured. With respect to this system a moving clock loses time and a moving length contracts. The book then presents a definition of simultaneity for the other inertial frames without using the velocity of light. To do so it employs the known reciprocity principle, which in this context serves to provide a definition of simultaneity in the other inertial frames. As a consequence, the Lorentz transformation is deduced and the universal constancy of light is established. With the help of a lattice model of the special theory of relativity the book provides a deeper understanding of the relativistic effects. Further, it discusses the key STR experiments and formulates and solves 54 problems in detail.