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Physics of the Lorentz group /

"Version: 20151101"--Title page verso."A Morgan & Claypool publication as part of IOP Concise Physics"--Title page verso.Includes bibliographical references.Preface -- 1. The Lorentz group and its representations -- 1.1. Generators of the Lorentz group -- 1.2. Two-by-two representation of the Lorentz group -- 1.3. Representations based on harmonic oscillators2. Wigner's little groups for internal space-time symmetries -- 2.1. Euler decomposition of Wigner's little group -- 2.2. The O(3)-like little group for massive particles -- 2.3. The E(2)-like little group for massless particles -- 2.4. The O(2, 1)-like little group for imaginary-mass particles -- 2.5. Summary3. Two-by-two representations of Wigner's little groups -- 3.1. Representations of Wigner's little groups -- 3.2. Lorentz completion of the little groups -- 3.3. Bargmann and Wigner decompositions -- 3.4. Conjugate transformations -- 3.5. Polarization of massless neutrinos -- 3.6. Scalars, four-vectors, and four-tensors4. One little group with three branches -- 4.1. One expression with three branches -- 4.2. Classical damped oscillators -- 4.3. Little groups in the light-cone coordinate system -- 4.4. Lorentz completion in the light-cone coordinate system5. Lorentz-covariant harmonic oscillators -- 5.1. Dirac's plan to construct Lorentz-covariant quantum mechanics -- 5.2. Dirac's forms of relativistic dynamics -- 5.3. Running waves and standing waves -- 5.4. Little groups for relativistic extended particles -- 5.5. Further properties of covariant oscillator wave functions -- 5.6. Lorentz contraction of harmonic oscillators -- 5.7. Feynman's rest of the Universe6. Quarks and partons in the Lorentz-covariant world -- 6.1. Lorentz-covariant quark model -- 6.2. Feynman's parton picture -- 6.3. Proton structure function -- 6.4. Proton form factor and Lorentz coherence -- 6.5. Coherence in momentum-energy space -- 6.6. Hadronic temperature and boiling quarks7. Coupled oscillators and squeezed states of light -- 7.1. Two coupled oscillators -- 7.2. Squeezed states of light -- 7.3. O(3, 2) symmetry from Dirac's coupled oscillators -- 7.4. O(3, 3) symmetry from Dirac matrices -- 7.5. Non-canonical transformations in quantum mechanics -- 7.6. Entropy and the expanding Wigner phase space8. Lorentz group in ray optics -- 8.1. Group of ABCD-matrices -- 8.2. Equi-diagonalization of the ABCD-matrix -- 8.3. Decomposition of the ABCD-matrix -- 8.4. Laser cavities -- 8.5. Multilayer optics -- 8.6. Camera optics9. Polarization optics -- 9.1. Jones vectors -- 9.2. Squeeze and phase shift -- 9.3. Rotation of the polarization axes -- 9.4. Optical activities10. Poincar?e sphere -- 10.1. Coherency matrix -- 10.2. Entropy problem -- 10.3. Symmetries derivable from the Poincar?e sphere -- 10.4. O(3, 2) symmetry.This book explains the Lorentz mathematical group in a language familiar to physicists. While the three-dimensional rotation group is one of the standard mathematical tools in physics, the Lorentz group of the four-dimensional Minkowski space is still very strange to most present-day physicists. It plays an essential role in understanding particles moving at close to light speed and is becoming the essential language for quantum optics, classical optics, and information science. The book is based on papers and books published by the authors on the representations of the Lorentz group based on harmonic oscillators and their applications to high-energy physics and to Wigner functions applicable to quantum optics. It also covers the two-by-two representations of the Lorentz group applicable to ray optics, including cavity, multilayer and lens optics, as well as representations of the Lorentz group applicable to Stokes parameters and the Poincar?e sphere on polarization optics.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader.Sibel Baskal is a Professor of Physics at the Middle East Technical University in Ankara, Turkey where she researches manifestations of Poincar?e, Lorentz, and Wigner's little groups and of group contractions in optical sciences. She also researches current problems in classical field theories such as sigma models, non-abelian gauge fields and general relativity, with a particular focus on alternative approaches. Young S. Kim is Professor Emeritus in the Department of Physics, University of Maryland. His research interests have focused on elementary particle theory, the foundations of quantum mechanics, and the Lorentz group applicable to other areas of physics including quantum optics, condensed matter physics, and classical mechanics. Marilyn E. Noz is a Research Professor and Professor Emerita in the Department of Radiology at the New York University School of Medicine. Her primary research focus is the integration of functional and anatomical (multi-modality) imaging into clinical practice. Image registration is used across multiple images, initially 2D, now 3D. Since 1971, her collaboration with Professor Kim in elementary particle physics has resulted in three books and more than 40 journal publications.Title from PDF title page (viewed on December 1, 2015).

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Publisher
: .,
Collation
1 online resource (various pagings) :illustrations (some color).
Language
English
ISBN/ISSN
9781681742540
Classification
512/.2
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Edition
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Subject(s)
SCIENCE / Physics / Mathematical & Computational.
Mathematical physics.
SCIENCE / Physics / Quantum Theory.
Lorentz groups.
Rotation groups.
Quantum Physics.
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