Mathematics – Group Theory
Scientific paper
Oct 1975
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975nyasa.262..241t&link_type=abstract
(AAS, American Physical Society, and New York Academy of Sciences, Texas Symposium on Relativistic Astrophysics, 7th, Dallas, Te
Mathematics
Group Theory
24
Gravitation Theory, Lorentz Transformations, Relativity, Space-Time Functions, Astronomical Models, Curvature, Group Theory, Lie Groups, Torsion, Variational Principles
Scientific paper
Commutation relations among the fundamental vector fields defined by a linear (metric) connection on a Lorentz bundle generalize the corresponding relations for the Lie algebra of the Poincare group. An analogy between torsion and curvature in relation to translations and rotations in the tangent spaces of the 4-dimensional manifold is pointed out. The commutation relationships define a 10-dimensional Lie algebra for a space of constant curvature without torsion. Compatibility of the metric and affine structures in space-time is argued. The article briefly reviews work by the Warsaw group on the Einstein-Cartan theory of gravitation as influenced by spin.
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