Towards an Ashtekar Formalism in Eight Dimensions
نویسنده
چکیده
We investigate the possibility of extending the Ashtekar theory to eight dimensions. Our approach relies on two notions: the octonionic structure and the MacDowell-Mansouri formalism generalized to a spacetime of signature 1+7. The key mathematical tool for our construction is the self-dual (antiselfdual) four-rank fully antisymmetric octonionic tensor. Our results may be of particular interest in connection with a possible formulation of M−theory via matroid theory. Pacs numbers: 04.60.-m, 04.65.+e, 11.15.-q, 11.30.Ly February, 2005 1 [email protected]
منابع مشابه
The Self-dual Action of the Ashtekar Formalism Revisited
Different aspects of the self-dual (anti-self-dual) action of the Ashtekar canonical formalism are revisited. In particular, we study the equivalences and differences between the various versions of such an action. Our analysis may be useful for the development of Ashtekar formalism in eight dimensions. Pacs numbers: 04.60.-m, 04.65.+e, 11.15.-q, 11.30.Ly November, 2004 1 [email protected]
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