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, D., Penati, S., Tamassia, L. (2003). Non(anti)commutative superspace. CLASSICAL AND QUANTUM GRAVITY, 20(13), 2905-2916 [10.1088/0264-9381/20/13/333].

Non(anti)commutative superspace

PENATI, SILVIA;
2003

Abstract

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
Articolo in rivista - Articolo scientifico
Superspace, nonanticommutative algebra
English
2003
20
13
2905
2916
none
Klemm, D., Penati, S., Tamassia, L. (2003). Non(anti)commutative superspace. CLASSICAL AND QUANTUM GRAVITY, 20(13), 2905-2916 [10.1088/0264-9381/20/13/333].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/3273
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