IJPAM: Volume 49, No. 4 (2008)


S.R.M.M Roveda$^1$, M.F. Borges$^2$
$^1$UNESP - Sao Paulo State University
Sorocaba Campus, Sorocaba, 18087-180, BRAZIL
e-mail: sandra@sorocaba.unesp.br
$^2$UNESP - Sao Paulo State University
S.J. Rio Preto Campus
S.J. Rio Preto, 15054-000, BRAZIL
e-mail: borges@ibilce.unesp.br

Abstract.The main purpose standing behind the group manifold approach to gravity and supergravity theories, is the need for describing forces of nature by means of non-Riemannian geometries, and to examine their physical contents in terms of a vierbein formalism. Motivated by the close relationship that is connecting quantum gravity and Yang-Mills theory in the non-perturbative strings theory framework, we have extended the group manifold geometrical scenario by introducing a general gauge group $\mathcal{G}$. Although we are still deeply rooted in Regge's ideas that led to the group-manifold approach, our work has had its own particularities: here dynamics is controlled by geometry in the sense that first curvatures and Bianchi identities were established and then the Lagrangian is worked out. Using the basic tools of exterior forms and exterior derivatives, gravitation and its extension as a Yang-Mills theory is then described on a group manifold $G$. $G$ has the same relationship to the Poincaré group, as curved spacetime does to Minkowski spacetime, except that the existence of a metric is now replaced by assumptions about the vierbein. In this paper, we synthesize the main features of the extended geometrical scenario that we have established and discuss perspectives for the nearest future.

Received: August 14, 2008

AMS Subject Classification: 83DO5, 83C99, 51PO5

Key Words and Phrases: Einstein-Cartan formulation, Cartan's gravity, Yang-Mills theory, group manifold

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 49
Issue: 4