Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-04-23
Class.Quant.Grav. 20 (2003) 2905-2916
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 16 pages, shortened version to appear in Class. Quant. Grav
Scientific paper
10.1088/0264-9381/20/13/333
We investigate the most general non(anti)commutative geometry in N=1 four-dimensional superspace, invariant under the classical (i.e., undeformed) supertranslation group. We find that a nontrivial non(anti)commutative superspace geometry compatible with supertranslations exists with non(anti)commutation parameters which may depend on the spinorial coordinates. The algebra is in general nonassociative. Imposing associativity introduces additional constraints which however allow for nontrivial commutation relations involving fermionic coordinates. We obtain explicitly the first three terms of a series expansion in the deformation parameter for a possible associative *-product. We also consider the case of N=2 euclidean superspace where the different conjugation relations among spinorial coordinates allow for a more general supergeometry.
Klemm Dietmar
Penati Silvia
Tamassia Laura
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