A Geometrical Interpretation of Grassmannian Coordinates

Details A Geometrical Interpretation of Grassmannian Coordinates A Geometrical Interpretation of Grassmannian Coordinates

2001-04-15

arxiv.org/abs/hep-th/0104129v2

Gen.Rel.Grav. 34 (2002) 1267-1275

Physics

High Energy Physics

High Energy Physics - Theory

essential changes : mathematical definitions, proofs and new references are added

Scientific paper

A geometrical interpretation of Grassmannian anticommuting coordinates is given. They are taken to represent an indefiniteness inherent in every spacetime point on the level of the spacetime foam. This indeterminacy is connected with the fact that in quantum gravity in some approximation we do not know the following information : are two points connected by a quantum wormhole or not ? It is shown that: (a) such indefiniteness can be represented by Grassmanian numbers, (b) a displacement of the wormhole mouth is connected with a change of the Grassmanian numbers (coordinates). In such an interpretation of supersymmetry the corresponding supersymmetrical fields must be described in an invariant manner on the background of the spacetime foam.

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