Oriented matroid theory and loop quantum gravity in (2+2) and eight dimensions
J.A. Nieto
Mathematical, Computational & Modeling Science Center, Arizona State University, PO Box 871904, Tempe, AZ 85287, USA. Facultad de Ciencias Físico-Matemáticas de la Universidad Autónoma de Sinaloa, 80010, Culiacán Sinaloa, México. Departamento de Investigación en Física de la Universidad de Sonora, 83000, Hermosillo Sonora, México.
Recibido el 18 de noviembre de 2010; ]]> aceptado el 26 de julio de 2011
Abstract
We establish a connection between oriented matroid theory and loop quantum gravity in (2+2) (two time and two space dimensions) and 8-dimensions. We start by observing that supersymmetry implies that the structure constants of the real numbers, complex numbers, quaternions and octonions can be identified with the chirotope concept. This means, among other things, that normed divisions algebras, which are only possible in 1,2, 4 or 8-dimensions, are linked to oriented matroid theory. Therefore, we argue that the possibility for developing loop quantum gravity in 8-dimensions must be taken as important alternative. Moreover, we show that in 4-dimensions, loop quantum gravity theories in the (1+3) or (0+4) signatures are not the only possibilities. In fact, we show that loop quantum gravity associated with the (2+2)-signature may also be an interesting physical structure.
Keywords: Loop quantum gravity; eight dimensions; (2+2)-dimensions.
PACS: 04.60.-m; 04.65.+e; 11.15.-q; 11.30.Ly
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