Group theory and general relativity : representations of the Lorentz group and their applications to the gravitational field /

This is the only book on the subject of group theory and Einstein's theory of gravitation. It contains an extensive discussion on general relativity from the viewpoint of group theory and gauge fields. It also puts together in one volume many scattered, original works, on the use of group theor...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Carmeli, Moshe, 1933-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Singapore ; River Edge, NJ : World Scientific, ©2000.
Temas:
Lorentz transformations.
Transformations de Lorentz.
SCIENCE > Physics > Relativity.
Darstellung > Mathematik
Anwendung
Gravitationsfeld
Allgemeine Relativitätstheorie
Gruppentheorie
Lorentz-Gruppe
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 1. The rotation group. 1.1. The three-dimensional pure rotation group. 1.2. The group SU[symbol]. 1.3. Invariant integral over the groups O[symbol] and SU[symbol]. 1.4. Representations of the groups O[symbol] and SU[symbol]. 1.5. Matrix elements of irreducible representations. 1.6. Differential operators of infinitesimal rotations
  • 2. The Lorentz group. 2.1. Infinitesimal Lorentz matrices. 2.2. Infinitesimal Operators. 2.3. Representations of the group L
  • 3. Spinor representation of the Lorentz group. 3.1. The group SL(2, C) and the Lorentz group. 3.2. Spinor representation of the group SL(2, C). 3.3. Infinitesimal operators of the spinor representation
  • 4. Principal series of representations of SL(2, C). 4.1. Linear spaces of representations. 4.2. The group operators. 4.3. SU[symbol] description of the principal series. 4.4. Comparison with the infinitesimal approach
  • 5. Complementary series of representations of SL(2, C). 5.1. Realization of the complementary series. 5.2. SU[symbol] description of the complementary series. 5.3. Operator formulation
  • 6. Complete series of representations of SL(2, C). 6.1. Realization of the complete series. 6.2. Complete series and spinors. 6.3. Unitary representations case. 6.4. Harmonic analysis on the group SL(2, C)
  • 7. Elements of general relativity theory. 7.1. Riemannian geometry. 7.2. Principle of equivalence. 7.3. Principle of general covariance. 7.4. Gravitational field equations. 7.5. Solutions of Einstein's field equations. 7.6. Experimental tests of general relativity. 7.7. Equations of motion
  • 8. Spinors in general relativity. 8.1. Connection between spinors and tensors. 8.2. Maxwell, Weyl and Riemann spinors. 8.3. Classification of Maxwell spinor. 8.4. Classification of Weyl spinor
  • 9. SL(2, C) gauge theory of the gravitational field: the Newman-Penrose equations. 9.1. Isotopic spin and gauge fields. 9.2. Lorentz invariance and the gravitational field. 9.3. SL(2, C) invariance and the gravitational field. 9.4. Gravitational field equations
  • 10. Analysis of the gravitational field. 10.1. Geometrical interpretation. 10.2. Choice of coordinate system. 10.3. Asymptotic behavior
  • 11. Some exact solutions of the gravitational field equations. 11.1. Solutions containing hypersurface orthogonal geodesic rays. 11.2. The NUT-Taub metric. 11.3. Type D vacuum metrics
  • 12. The Bondi-Metzner-Sachs group. 12.1. The Bondi-Metzner-Sachs group. 12.2. The structure of the Bondi-Metzner-Sachs Group.

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