Computer Science
Scientific paper
Jun 1991
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991phdt........19y&link_type=abstract
Thesis (PH.D.)--UNIVERSITY OF MARYLAND COLLEGE PARK, 1991.Source: Dissertation Abstracts International, Volume: 52-09, Section:
Computer Science
Scientific paper
In this thesis, Einstein-Cartan theories in (4 + n)-dimensions are studied. These are theories of the metric-compatible connections that include the metric as well as the torsion in higher dimensions. As a way of dimensional reduction to four dimensions, we impose an n-dimensional isometry on the multi-dimensional metric and torsion. This isometry endows the underlying geometry with the structure of a principal fibre bundle over a four dimensional base manifold, with the group space as an n -dimensional fibre at each space-time point. We consider the (4 + n)-dimensional Einstein-Hilbert -Cartan action defined on the bundle, and study their dynamics in various context, i.e. in cosmology, in asymptotically flat cases (in the four dimensional sense) as well as in gauge theories. We shall present some exact solutions of the higher dimensional field equations, and discuss them in detail. In addition we derive a whole series of both the CP_{N-1} non -linear sigma models and their grassmannian generalizations for certain classes of internal metrics. It is hoped that these derivations render a better understanding of theories of these non-linear sigma models.
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