Quantum Mechanics With Non Unitary Symmetries

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Quantum Mechanics with Non-Unitary Symmetries

Bojan Bistrovic
Quantum Mechanics with Non Unitary Symmetries Book PDF

Author : Bojan Bistrovic
Publisher : Marsonia Press LLC
Page : 551 pages
File Size : 53,6 Mb
Release : 2020-04-22
Category : Science
ISBN : 9781734919912

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Quantum Mechanics with Non-Unitary Symmetries by Bojan Bistrovic Pdf

This book shows that with minimal modifications of postulates of non-relativistic quantum mechanics to allow for non-unitary representations of symmetry groups (Lorentz group in particular), one achieves a fully relativistic quantum theory without any of the issues (like negative energies, etc.) that led to the second quantization and QFT. It is shown that quite a few phenomena in elementary particle physics (like for example neutral kaon mixing, CP symmetry and it's supposed breaking) can be explained purely as a consequence of relativistic invariance and relativistic invariance alone. It is shown that by categorizing mesons via the representation of Lorentz group they belong to, one can explain a lot of their properties, as well as a lot of discrepancies in the particle data tables. It is also shown that based on properties of Lorentz representations of products of meson decays, a lot of excited states listed in PDG tables are really several different excitations with similar masses. Relativistic treatment of bound states in momentum space is developed and used to calculate decay widths of various composite particles like Positronium or mesons, and then those decay widths are used to calculate various properties of quarks (like their masses or charges) that were previously misunderstood. In particular, it is shown that quarks are actually quite heavy (around 3.5GeV for up/down quarks) and that while Lorentz invariance allows both fractional values (2/3, -1/3) as well as integer values (2,1), based on (very sparse) available experimental data, integer quark charges are more consistent with observed decay widths than fractional charges.

Quantum Mechanics with Non-Unitary Symmetries

Bojan Bistrovi?
Quantum Mechanics with Non Unitary Symmetries Book PDF

Author : Bojan Bistrovi?
Publisher : Unknown
Page : 128 pages
File Size : 50,6 Mb
Release : 2020-04-16
Category : Electronic
ISBN : 1734919906

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Quantum Mechanics with Non-Unitary Symmetries by Bojan Bistrovi? Pdf

This book shows that with minimal modifications of postulates of non-relativistic quantum mechanics to allow for non-unitary representations of symmetry groups (Lorentz group in particular), one achieves a fully relativistic quantum theory without any of the issues (like negative energies, etc.) that led to the second quantization and QFT. It is shown that quite a few phenomena in elementary particle physics (like for example neutral kaon mixing, CP symmetry and it's supposed breaking) can be explained purely as a consequence of relativistic invariance and relativistic invariance alone.It is shown that by categorizing mesons via the representation of Lorentz group they belong to, one can explain a lot of their properties, as well as a lot of discrepancies in the particle data tables. It is also shown that based on properties of Lorentz representations of products of meson decays, a lot of excited states listed in PDG tables are really several different excitations with similar masses.Relativistic treatment of bound states in momentum space is developed and used to calculate decay widths of various composite particles like Positronium or mesons, and then those decay widths are used to calculate various properties of quarks (like their masses or charges) that were previously misunderstood.In particular, it is shown that quarks are actually quite heavy (around 3.5GeV for up/down quarks) and that while Lorentz invariance allows both fractional values (2/3, -1/3) as well as integer values (2,1), based on (very sparse) available experimental data, integer quark charges are more consistent with observed decay widths than fractional charges.

Symmetries in Quantum Physics

U. Fano,A. R.P. Rau
Symmetries in Quantum Physics Book PDF

Author : U. Fano,A. R.P. Rau
Publisher : Elsevier
Page : 349 pages
File Size : 51,9 Mb
Release : 1996-06-17
Category : Science
ISBN : 9780080542171

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Symmetries in Quantum Physics by U. Fano,A. R.P. Rau Pdf

This text focuses on the physics of symmetries, developing symmetries and transformations through concrete physical examples and contexts rather than presenting the information axiomatically, mathematically, and abstractly. Readers are introduced gradually to advanced mathematical procedures, including the Wigner and Racah algebras and their applications to various symmetry groups. The book also includes some of the latest research on the use of non-invariance and non-compact groups in the consideration of relativistic and many-particle problems of atoms and nuclei. This book is an updated replacement for the text Irreducible Tensorial Sets (Academic Press, 1959). Parts A and B of the present book grew out of occasional lectures in the intervening decades at the University of Chicago, where it became neccessary to update or elaborate upon certain points. Part C has been built more recently to deal with innovations and new information in the field of mathematical physics. The book as a whole develops the subject of symmetry from a physical point of view, allowing students and researchers to gain new insight on their subject. This book can be used both as a text and as a reference by students and scientists in the field. Adapts and extends the earlier Irreducible Tensor Sets (Academic Press, 1959) to classroom use Extends to multi-particle systems and relativity Includes problems in each chapter for homework assignments Embraces the latest research on non-invariance groups

Symmetries in Quantum Mechanics

M Chaichian,R Hagedorn
Symmetries in Quantum Mechanics Book PDF

Author : M Chaichian,R Hagedorn
Publisher : CRC Press
Page : 349 pages
File Size : 55,5 Mb
Release : 2023-07-21
Category : Science
ISBN : 9781000950946

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Symmetries in Quantum Mechanics by M Chaichian,R Hagedorn Pdf

Symmetries in Quantum Mechanics: From Angular Momentum to Supersymmetry (PBK) provides a thorough, didactic exposition of the role of symmetry, particularly rotational symmetry, in quantum mechanics. The bulk of the book covers the description of rotations (geometrically and group-theoretically) and their representations, and the quantum theory of angular momentum. Later chapters introduce more advanced topics such as relativistic theory, supersymmetry, anyons, fractional spin, and statistics. With clear, in-depth explanations, the book is ideal for use as a course text for postgraduate and advanced undergraduate students in physics and those specializing in theoretical physics. It is also useful for researchers looking for an accessible introduction to this important area of quantum theory.

Non-Relativistic Quantum Theory

Kai S Lam
Non Relativistic Quantum Theory Book PDF

Author : Kai S Lam
Publisher : World Scientific Publishing Company
Page : 460 pages
File Size : 41,7 Mb
Release : 2009-08-24
Category : Science
ISBN : 9789813107489

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Non-Relativistic Quantum Theory by Kai S Lam Pdf

This textbook is mainly for physics students at the advanced undergraduate and beginning graduate levels, especially those with a theoretical inclination. Its chief purpose is to give a systematic introduction to the main ingredients of the fundamentals of quantum theory, with special emphasis on those aspects of group theory (spacetime and permutational symmetries and group representations) and differential geometry (geometrical phases, topological quantum numbers, and Chern–Simons Theory) that are relevant in modern developments of the subject. It will provide students with an overview of key elements of the theory, as well as a solid preparation in calculational techniques.

Symmetries in Science

Bruno Gruber
Symmetries in Science Book PDF

Author : Bruno Gruber
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781468438338

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Symmetries in Science by Bruno Gruber Pdf

Southern Illinois University at Carbondale undertook to honor Albert Einstein as scientist and as humanitarian in commemo ration of his lOOth birthday during an "Albert Einstein Centennial Week", February 23 - March 2, 1979. During the course of this week two Symposia were held, entitled "Symmetries in Science" and "Einstein: Humanities Conscience", in addition to cultural and social activities honoring Einstein. This volume presents the Symposium "Symmetries in Science". It reflects the outstanding response that was given to our "Albert Einstein Centennial Week" by the international community of scientists. The motivation to have a celebration honoring Albert Einstein at Southern Illinois University at Carbondale was supplied by Dr. Paul A. Schilpp, the editor of the "Library of Living Philo sophers". Albert Einstein has contributed to this series with his autobiographical notes, a kind of autobiography of his scientific life, in a volume entitled "Einstein: Scientist-Philosopher", the most popular among all the outstanding volumes of this series. Dr. Paul A. Schilpp's presence at Southern Illinois University at Carbondale provided a natural link for an Einstein Celebration as a kind of a continuation of the contribution he made to mankind through the Einstein volume of his "Library of Living Philosophers".

Reflections on Quanta, Symmetries, and Supersymmetries

V.S. Varadarajan
Reflections on Quanta Symmetries and Supersymmetries Book PDF

Author : V.S. Varadarajan
Publisher : Springer Science & Business Media
Page : 242 pages
File Size : 51,5 Mb
Release : 2011-05-20
Category : Mathematics
ISBN : 9781441906670

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Reflections on Quanta, Symmetries, and Supersymmetries by V.S. Varadarajan Pdf

This is a collection of essays based on lectures that author has given on various occasions on foundation of quantum theory, symmetries and representation theory, and the quantum theory of the superworld created by physicists. The lectures are linked by a unifying theme: how the quantum world and superworld appear under the lens of symmetry and supersymmetry. In the world of ultra-small times and distances such as the Planck length and Planck time, physicists believe no measurements are possible and so the structure of spacetime itself is an unknown that has to be first understood. There have been suggestions (Volovich hypothesis) that world geometry at such energy regimes is non-archimedian and some of the lectures explore the consequences of such a hypothesis. Ultimately, symmetries and supersymmetries are described by the representation of groups and supergroups. The author's interest in representation is a lifelong one and evolved slowly, and owes a great deal to conversations and discussions he had with George Mackey and Harish-Chandra. The book concludes with a retrospective look at these conversations.

Group Theory in Quantum Mechanics

Volker Heine
Group Theory in Quantum Mechanics Book PDF

Author : Volker Heine
Publisher : Elsevier
Page : 479 pages
File Size : 54,6 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.

Quantum Mechanics

Walter Greiner,Berndt Müller
Quantum Mechanics Book PDF

Author : Walter Greiner,Berndt Müller
Publisher : Springer Science & Business Media
Page : 538 pages
File Size : 53,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642579769

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Quantum Mechanics by Walter Greiner,Berndt Müller Pdf

Greiner's lectures, which underlie these volumes, are internationally noted for their clarity, their completeness and for the effort that he has devoted to making physics an integral whole; his enthusiasm for his science is contagious and shines through almost every page. These volumes represent only a part of a unique and Herculean effort to make all of theoretical physics accessible to the interested student. Beyond that, they are of enormous value to the professional physicist and to all others working with quantum phenomena. Again and again the reader will find that, after dipping into a particular volume to review a specific topic, he will end up browsing, caught up by often fascinating new insights and developments with which he had not previously been familiar. Having used a number of Greiner's volumes in their original German in my teaching and research at Yale, I welcome these new and revised English translations and would recommend them enthusiastically to anyone searching for a coherent overview of physics.

New Symmetry Principles in Quantum Field Theory

J. Frölich,Gerard 't Hooft,Arthur Jaffe,Gerhard Mack,Pronob K. Mitter,Raymond Stora
New Symmetry Principles in Quantum Field Theory Book PDF

Author : J. Frölich,Gerard 't Hooft,Arthur Jaffe,Gerhard Mack,Pronob K. Mitter,Raymond Stora
Publisher : Springer Science & Business Media
Page : 528 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461534723

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New Symmetry Principles in Quantum Field Theory by J. Frölich,Gerard 't Hooft,Arthur Jaffe,Gerhard Mack,Pronob K. Mitter,Raymond Stora Pdf

Soon after the discovery of quantum mechanics, group theoretical methods were used extensively in order to exploit rotational symmetry and classify atomic spectra. And until recently it was thought that symmetries in quantum mechanics should be groups. But it is not so. There are more general algebras, equipped with suitable structure, which admit a perfectly conventional interpretation as a symmetry of a quantum mechanical system. In any case, a "trivial representation" of the algebra is defined, and a tensor product of representations. But in contrast with groups, this tensor product needs to be neither commutative nor associative. Quantum groups are special cases, in which associativity is preserved. The exploitation of such "Quantum Symmetries" was a central theme at the Ad vanced Study Institute. Introductory lectures were presented to familiarize the participants with the al gebras which can appear as symmetries and with their properties. Some models of local field theories were discussed in detail which have some such symmetries, in par ticular conformal field theories and their perturbations. Lattice models provide many examples of quantum theories with quantum symmetries. They were also covered at the school. Finally, the symmetries which are the cause of the solubility of inte grable models are also quantum symmetries of this kind. Some such models and their nonlocal conserved currents were discussed.

Quantum Theory And Symmetries - Proceedings Of The International Symposium

Vladimir K Dobrev,Heinz-dietrich Doebner,J-d Hennig,W Lucke
Quantum Theory And Symmetries Proceedings Of The International Symposium Book PDF

Author : Vladimir K Dobrev,Heinz-dietrich Doebner,J-d Hennig,W Lucke
Publisher : World Scientific
Page : 641 pages
File Size : 51,9 Mb
Release : 2000-05-05
Category : Science
ISBN : 9789814543040

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Quantum Theory And Symmetries - Proceedings Of The International Symposium by Vladimir K Dobrev,Heinz-dietrich Doebner,J-d Hennig,W Lucke Pdf

This volume gives a representative survey of recent developments in relativistic and non-relativistic quantum theory, which are related to the application of symmetries in their most general sense. The corresponding mathematical notions are centered upon groups, algebras and their generalizations, and are applied in interaction with topology, differential geometry, functional analysis and related fields. Special emphasis is on results in the following areas: quantization methods, nonlinear evolution equations, foundation of quantum physics, algebraic quantum field theory, gauge and string theories, quantum information, quantum groups, discrete symmetries.

Quantum Symmetries

Guillaume Aubrun,Adam Skalski,Roland Speicher
Quantum Symmetries Book PDF

Author : Guillaume Aubrun,Adam Skalski,Roland Speicher
Publisher : Springer
Page : 119 pages
File Size : 43,7 Mb
Release : 2017-10-11
Category : Mathematics
ISBN : 9783319632063

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Quantum Symmetries by Guillaume Aubrun,Adam Skalski,Roland Speicher Pdf

Providing an introduction to current research topics in functional analysis and its applications to quantum physics, this book presents three lectures surveying recent progress and open problems. A special focus is given to the role of symmetry in non-commutative probability, in the theory of quantum groups, and in quantum physics. The first lecture presents the close connection between distributional symmetries and independence properties. The second introduces many structures (graphs, C*-algebras, discrete groups) whose quantum symmetries are much richer than their classical symmetry groups, and describes the associated quantum symmetry groups. The last lecture shows how functional analytic and geometric ideas can be used to detect and to quantify entanglement in high dimensions. The book will allow graduate students and young researchers to gain a better understanding of free probability, the theory of compact quantum groups, and applications of the theory of Banach spaces to quantum information. The latter applications will also be of interest to theoretical and mathematical physicists working in quantum theory.

Symmetries in Science X

Bruno Gruber,Michael Ramek
Symmetries in Science X Book PDF

Author : Bruno Gruber,Michael Ramek
Publisher : Springer Science & Business Media
Page : 446 pages
File Size : 51,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781489915375

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Symmetries in Science X by Bruno Gruber,Michael Ramek Pdf

Proceedings an International Symposium held in Bregenz, Austria, July 13-18, 1997

Symmetries and Group Theory in Particle Physics

Giovanni Costa,Gianluigi Fogli
Symmetries and Group Theory in Particle Physics Book PDF

Author : Giovanni Costa,Gianluigi Fogli
Publisher : Springer
Page : 291 pages
File Size : 51,6 Mb
Release : 2012-02-03
Category : Science
ISBN : 9783642154829

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Symmetries and Group Theory in Particle Physics by Giovanni Costa,Gianluigi Fogli Pdf

Symmetries, coupled with the mathematical concept of group theory, are an essential conceptual backbone in the formulation of quantum field theories capable of describing the world of elementary particles. This primer is an introduction to and survey of the underlying concepts and structures needed in order to understand and handle these powerful tools. Specifically, in Part I of the book the symmetries and related group theoretical structures of the Minkowskian space-time manifold are analyzed, while Part II examines the internal symmetries and their related unitary groups, where the interactions between fundamental particles are encoded as we know them from the present standard model of particle physics. This book, based on several courses given by the authors, addresses advanced graduate students and non-specialist researchers wishing to enter active research in the field, and having a working knowledge of classical field theory and relativistic quantum mechanics. Numerous end-of-chapter problems and their solutions will facilitate the use of this book as self-study guide or as course book for topical lectures.

Physics from Symmetry

Jakob Schwichtenberg
Physics from Symmetry Book PDF

Author : Jakob Schwichtenberg
Publisher : Springer
Page : 287 pages
File Size : 50,8 Mb
Release : 2017-12-01
Category : Science
ISBN : 9783319666310

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Physics from Symmetry by Jakob Schwichtenberg Pdf

This is a textbook that derives the fundamental theories of physics from symmetry. It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived. As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations. Thanks to the input of readers from around the world, this second edition has been purged of typographical errors and also contains several revised sections with improved explanations.