Oriented matroid theory and loop quantum gravity in (2+2) and eight dimensions

Details Oriented matroid theory and loop quantum gravity in (2+2) and eight dimensions Oriented matroid theory and loop quantum gravity in (2+2) and eight dimensions

2010-03-24

arxiv.org/abs/1003.4750v1

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, Latex

Scientific paper

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.

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