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Physics of the Lorentz grou...
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
Monografía
monografia Rebiun19049264 https://catalogo.rebiun.org/rebiun/record/Rebiun19049264 m eo d cr cn |||m|||a 151201s2015 caua ob 000 0 eng d 1-68174-190-3 1-68174-254-3 10.1088/978-1-6817-4254-0 doi CBUC 991038667819706706 CBUC 991001722959706708 CaBNVSL eng rda CaBNVSL CaBNVSL PHU bicssc PHQ bicssc SCI040000 bisacsh SCI057000 bisacsh 512/.2 23 Baskal, Sibel author Physics of the Lorentz group Sibel Baskal, Young S. Kim, Marilyn E. Noz IOP concise physics San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) Morgan & Claypool Publishers [2015] San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) Morgan & Claypool Publishers Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) IOP Publishing [2015] Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) IOP Publishing 1 online resource (various pagings) illustrations (some color) 1 online resource (various pagings) Text rdacontent electronic isbdmedia online resource rdacarrier IOP concise physics 2053-2571 "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 oscillators 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 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 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 Poincaré, 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 Lorentz groups Rotation groups Mathematical physics SCIENCE / Physics / Mathematical & Computational. bicssc Mathematical Physics. bisacsh Quantum Physics. bisacsh SCIENCE / Physics / Quantum Theory. bicssc Kim, Y. S. author Noz, Marilyn E. author Morgan & Claypool Publishers publisher Institute of Physics (Great Britain) publisher IOP concise physics