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Physics of the Lorentz group
Údaje o názvu Physics of the Lorentz group / Sibel Bașkal, Young S. Kim, Marilyn E. Noz. [elektronický zdroj] Nakladatel San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) : Morgan & Claypool Publishers, [2015] Distributor Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2015] Fyz.popis 1 online resource (various pagings) : illustrations (some color). ISBN 9781681742540 (online) 9781681741260 mobi Edice [IOP release 2] IOP concise physics, ISSN 2053-2571 Poznámka "Version: 20151101"--Title page verso. "A Morgan & Claypool publication as part of IOP Concise Physics"--Title page verso. Poznámky o skryté bibliografii a rejstřících Includes bibliographical references. Úplný obsah 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 oscillators Poznámka o obsahu 2. 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. Summary. 3. 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-tensors. 4. 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 system. 5. 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 Universe. 6. 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 quarks. 7. 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 space. 8. 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 optics. 9. Polarization optics -- 9.1. Jones vectors -- 9.2. Squeeze and phase shift -- 9.3. Rotation of the polarization axes -- 9.4. Optical activities. 10. Poincaré sphere -- 10.1. Coherency matrix -- 10.2. Entropy problem -- 10.3. Symmetries derivable from the Poincaré sphere -- 10.4. O(3, 2) symmetry. Poznámky k dostupnosti Přístup pouze pro oprávněné uživatele Poznámky Způsob přístupu: World Wide Web.. Požadavky na systém: Adobe Acrobat Reader. Dal.odpovědnost Kim, Y. S., Noz, Marilyn E., Dal.odpovědnost Morgan & Claypool Publishers, Institute of Physics (Great Britain), Předmět.hesla Lorentz groups. * Rotation groups. * Mathematical physics. * SCIENCE / Physics / Mathematical & Computational. * Mathematical Physics. * Quantum Physics. Forma, žánr SCIENCE / Physics / Quantum Theory. * elektronické knihy electronic books Země vyd. Kalifornie Jazyk dok. angličtina Druh dok. Elektronické knihy URL Plný text pro studenty a zaměstnance UPOL 
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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 Poincaré sphere on polarization optics.
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. Poincaré sphere -- 10.1. Coherency matrix -- 10.2. Entropy problem -- 10.3. Symmetries derivable from the Poincaré sphere -- 10.4. O(3, 2) symmetry.
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