Quantum Mechanics With Non Unitary Symmetries
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| Author | : Bojan Bistrovic |
| Publisher | : Marsonia Press LLC |
| Total Pages | : 551 |
| Release | : 2020-04-22 |
| Genre | : Science |
| ISBN | : 1734919914 |
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.
| Author | : Bojan Bistrovi? |
| Publisher | : |
| Total Pages | : |
| Release | : 2020-04-16 |
| Genre | : |
| ISBN | : 9781734919905 |
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.
| Author | : U. Fano |
| Publisher | : Elsevier |
| Total Pages | : 349 |
| Release | : 1996-06-17 |
| Genre | : Science |
| ISBN | : 0080542174 |
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
| Author | : Kai S Lam |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 458 |
| Release | : 2009-08-24 |
| Genre | : Science |
| ISBN | : 9813107480 |
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.
| Author | : Bruno Gruber |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 492 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1468438336 |
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".
| Author | : V.S. Varadarajan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 242 |
| Release | : 2011-05-20 |
| Genre | : Mathematics |
| ISBN | : 1441906673 |
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.
| Author | : Walter Greiner |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 538 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642579760 |
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.
| Author | : Jakob Schwichtenberg |
| Publisher | : Springer |
| Total Pages | : 294 |
| Release | : 2017-12-01 |
| Genre | : Science |
| ISBN | : 3319666312 |
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.
| Author | : Volker Heine |
| Publisher | : Elsevier |
| Total Pages | : 479 |
| Release | : 2014-05-15 |
| Genre | : Science |
| ISBN | : 1483152006 |
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.
| Author | : Olimpia Lombardi |
| Publisher | : Cambridge University Press |
| Total Pages | : 411 |
| Release | : 2019-04-11 |
| Genre | : Science |
| ISBN | : 1108473474 |
Offers a comprehensive and up-to-date volume on the conceptual and philosophical problems related to the interpretation of quantum mechanics.
