Physics of the Lorentz group /

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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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Bașkal, Sibel (Autor), Kim, Y. S. (Autor), Noz, Marilyn E. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) : Morgan & Claypool Publishers, [2015]
Colección:IOP (Series). Release 2.
IOP concise physics.
Temas:
Lorentz groups.
Rotation groups.
Mathematical physics.
SCIENCE / Physics / Mathematical & Computational.
Mathematical Physics.
Quantum Physics.
SCIENCE / Physics / Quantum Theory.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

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