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Physics of the Lorentz group : beyond high-energy physics and optics / / Sibel Baskal, Young S. Kim, Marilyn E. Noz.
| Physics of the Lorentz group : beyond high-energy physics and optics / / Sibel Baskal, Young S. Kim, Marilyn E. Noz. |
| Autore | Baskal Sibel |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : , : IOP Publishing, , [2021] |
| Descrizione fisica | 1 online resource (various pagings) : illustrations (some color) |
| Disciplina | 512/.2 |
| Collana | IOP ebooks |
| Soggetto topico |
Lorentz groups
Rotation groups Mathematical physics |
| ISBN |
9780750336062
0750336064 9780750336079 0750336072 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
1. Lorentz group and its representations -- 1.1. Generators of the Lorentz group -- 1.2. Two-by-two representation of the Lorentz group -- 1.3. Conformal representation of the Lorentz group -- 1.4. Representations of the Poincaré group -- 1.5. Representations of the Lorentz group based on harmonic oscillators -- 1.6. Wigner functions for the Lorentz group
2. Wigner's little groups for internal space-time symmetries -- 2.1. Euler decomposition of Wigner's little group -- 2.2. O(3)-like little group for massive particles -- 2.3. E(2)-like little group for massless particles -- 2.4. O(2, 1)-like little group for imaginary-mass particles -- 2.5. Further properties of Wigner's little groups -- 2.6. Little groups in the light-cone coordinate system 3. Group contractions -- 3.1. Contraction with squeeze transformations -- 3.2. Contractions of the O(3) rotation group -- 3.3. Contraction of the O(2, 1) Lorentz group -- 3.4. Contraction of the Lorentz group -- 3.5. Tangential spheres 4. Two-by-two representations of Wigner's little groups -- 4.1. Transformation properties of the energy-momentum four-vector -- 4.2. Two-by-two representations of Wigner's little groups -- 4.3. Lorentz completion of the little groups -- 4.4. Bargmann and Wigner decompositions -- 4.5. Conjugate transformations -- 4.6. One little group with three branches -- 4.7. Classical damped harmonic oscillator 5. Relativistic spinors and polarization of photons and neutrinos -- 5.1. Two-component spinors -- 5.2. Massive and massless particles -- 5.3. Dirac spinors and massless particles -- 5.4. Polarization of massless neutrinos -- 5.5. Scalars, vectors, tensors, and the polarization of photons 6. Lorentz-covariant harmonic oscillators -- 6.1. Dirac's plan to construct Lorentz-covariant quantum mechanics -- 6.2. Dirac's forms of relativistic dynamics -- 6.3. Running waves and standing waves -- 6.4. Little groups for relativistic extended particles -- 6.5. Further properties of covariant oscillator wave functions -- 6.6. Lorentz contraction of harmonic oscillators -- 6.7. Feynman's rest of the Universe 7. Quarks and partons in the Lorentz-covariant world -- 7.1. Lorentz-covariant quark model -- 7.2. Feynman's parton picture -- 7.3. Proton structure function -- 7.4. Proton form factor and Lorentz coherence -- 7.5. Coherence in energy-momentum space -- 7.6. Hadronic temperature and boiling quarks 8. Wigner functions and their symmetries -- 8.1. Symmetries and the uncertainty principle in the Wigner phase space -- 8.2. Four-dimensional phase space -- 8.3. Canonical transformations -- 8.4. SL(4, r) symmetry -- 8.5. Dirac matrices for O(3, 3) -- 8.6. O(3, 3) symmetry 9. Coupled harmonic oscillators and squeezed states of light -- 9.1. Coupled oscillators -- 9.2. Lorentz-covariant oscillators -- 9.3. Squeezed states of light -- 9.4. Further notes on squeezed states -- 9.5. O(3, 2) symmetry from Dirac's coupled oscillators -- 9.6. Canonical and non-canonical transformations from the coupled oscillators -- 9.7. Entropy and the expanding Wigner phase space 10. Special relativity from quantum mechanics? -- 10.1. Definition of the problem -- 10.2. Symmetries of the single oscillator -- 10.3. Symmetries from two oscillators -- 10.4. Contraction of O(3, 2) to the inhomogeneous Lorentz group 11. Lorentz group in ray optics -- 11.1. The group of ABCD matrices applied to ray optics -- 11.2. Equi-diagonalization of the ABCD matrix -- 11.3. Decomposition of the ABCD matrix -- 11.4. Laser cavities -- 11.5. Composition of lens and translation matrices -- 11.6. Optical beam propagation through multilayers -- 11.7. Camera optics 12. Polarization optics -- 12.1. Jones vectors -- 12.2. Squeeze transformation and phase shift -- 12.3. Rotation of the polarization axes -- 12.4. The SL(2, c) group content of polarization optics -- 12.5. Optical activities -- 12.6. Correspondence to space-time symmetries -- 12.7. More optical filters from E(2)-like groups 13. Poincaré sphere -- 13.1. Decoherence in polarization optics -- 13.2. Coherency matrix -- 13.3. Poincaré sphere -- 13.4. Two concentric Poincaré spheres -- 13.5. Symmetries derivable from the Poincaré sphere -- 13.6. O(3, 2) symmetry for energy couplings -- 13.7. Entropy problem Appendix A. Physics as art of synthesis -- A.1. Illustration of Hume, Kant, and Hegel -- A.2. Kant and Einstein -- A.3. Kantianism and Taoism -- A.4. Einstein and Hegel. |
| Record Nr. | UNINA-9911009166103321 |
Baskal Sibel
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| Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : , : IOP Publishing, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Rotations, quaternions, and double groups / Simon L. Altmann
| Rotations, quaternions, and double groups / Simon L. Altmann |
| Autore | Altmann, Simon L. |
| Pubbl/distr/stampa | Oxford [Oxfordshire] : Clarendon Press |
| Descrizione fisica | xiv, 317 p. : ill. ; 24 cm |
| Disciplina | 510.9 |
| Collana | Oxford science publications |
| Soggetto topico |
Rotation groups
Quaternions Finite groups Representations of groups |
| ISBN | 9780198553724 |
| Classificazione | LC QC174.17.R65 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction -- All you need to know about symmetries, matrices, and groups -- A primer on rotations and rotation matrices -- Rotations and angular momentum -- Tensor bases: introduction to spinors -- The bilinear transformation: introduction to SU(2), SU'(2), and rotations. More about spinors -- Rotations and SU(2). The stereographic projection -- Projective representations -- The geometry of rotations -- The topology of rotations -- The spinor representations -- The algebra of rotations: quaternions -- Double groups -- The irreducible representations of SO(3) -- Examples and applications -- Solutions to problems |
| Record Nr. | UNISALENTO-991003806839707536 |
|
Altmann, Simon L.
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| Oxford [Oxfordshire] : Clarendon Press | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Soggetto topico
-
Rotation groups
(2)
- Finite groups (1)
- Lorentz groups (1)
- Mathematical physics (1)
- Quaternions (1)