UID:
almahu_9948202084702882
Format:
1 online resource (various pagings) :
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illustrations (chiefly color).
ISBN:
9780750316149
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9780750316132
Series Statement:
[IOP release 6]
Content:
The Lorentz group which is the underlying scientific language for modern optics has been most notably used for understanding Einstein's special relativity. By using a simplified approach of two-by-two matrices and Wigner functions, this book provides a basic and novel approach to classical and quantum optics, making these often-difficult subjects more transparent to the reader. Written by three experts in the field, Professors Sibel Başkal, Young S. Kim, and Marilyn E Noz, this book will give the reader a comprehensive overview of how fundamental issues in quantum mechanics can be approached using various optical instruments, Wigner functions, and quantum entanglement.
Note:
"Version: 20190601"--Title page verso.
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1. Forms of quantum mechanics -- 1.1. The Schrödinger and Heisenberg pictures -- 1.2. Interaction picture -- 1.3. Density-matrix formulation of quantum mechanics -- 1.4. Further contents of Heisenberg's commutation relations
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2. Lorentz group and its representations -- 2.1. Lie algebra of the Lorentz group -- 2.2. Two-by-two representation of the Lorentz group -- 2.3. Four-vectors in the two-by-two representation -- 2.4. Transformation properties in the two-by-two representation -- 2.5. Subgroups of the Lorentz group -- 2.6. Decompositions of the Sp(2) matrices -- 2.7. Bilinear conformal representation of the Lorentz group
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3. Internal space-time symmetries -- 3.1. Wigner's little groups -- 3.2. Little groups in the light-cone coordinate system -- 3.3. Two-by-two representation of the little groups -- 3.4. One expression with three branches -- 3.5. Classical damped oscillators
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4. Photons and neutrinos in the relativistic world of Maxwell and Wigner -- 4.1. The Lorentz group and Wigner's little groups -- 4.2. Massive and massless particles -- 4.3. Polarization of massless neutrinos -- 4.4. Scalars, vectors, tensors, and the polarization of photons
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5. Wigner functions -- 5.1. Basic properties of the Wigner phase-space distribution function -- 5.2. Time dependence of the Wigner function -- 5.3. Wave packet spread -- 5.4. Harmonic oscillators -- 5.5. Minimum uncertainty in phase space -- 5.6. Density matrix -- 5.7. Measurable quantities
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6. Coherent states of light -- 6.1. Phase-number uncertainty relation -- 6.2. Baker-Campbell-Hausdorff relation -- 6.3. Coherent states -- 6.4. Symmetry of coherent states -- 6.5. Coherent states in phase space -- 6.6. Single-mode squeezed states
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7. Squeezed states and their symmetries -- 7.1. Two-mode states -- 7.2. Unitary transformations -- 7.3. Symmetries of two-mode states -- 7.4. Dirac matrices and O(3,3) symmetry -- 7.5. Symmetries in phase space -- 7.6. Two coupled oscillators
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8. Entanglement and entropy -- 8.1. Density matrix and entropy -- 8.2. Two-by-two density matrices -- 8.3. Density matrix for two-oscillator states -- 8.4. Entropy for the two-mode state -- 8.5. Entangled excited states -- 8.6. Wigner functions and uncertainty relations
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9. Ray optics and optical activities -- 9.1. Ray optics using the group of ABCD matrices -- 9.2. Physical examples using ABCD matrices -- 9.3. Optical activities
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10. Polarization optics -- 10.1. Jones vector, phase shifters, and attenuators -- 10.2. New filters and possible applications -- 10.3. Non-orthogonal coordinate systems -- 11. Stokes parameters and Poincaré sphere -- 11.1. Polarization optics and decoherence -- 11.2. Coherency matrix and Stokes parameters -- 11.3. Poincaré sphere -- 11.4. The entropy problem -- 11.5. Further symmetries from the Poincaré sphere
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Appendix A. Covariant harmonic oscillators and the quark-parton puzzle -- A.1. The covariant harmonic oscillator -- A.2. Quark-parton puzzle.
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Also available in print.
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Mode of access: World Wide Web.
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System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.
Additional Edition:
Print version: ISBN 9780750316125
Language:
English
DOI:
10.1088/2053-2563/aafe78
URL:
https://iopscience.iop.org/book/978-0-7503-1614-9
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