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arxiv: hep-th/0604197 · v2 · submitted 2006-04-26 · ✦ hep-th

Quantum Mechanics in Non(Anti)Commutative Superspace

classification ✦ hep-th
keywords deformedquantumalgebraanticommutativeconservedfieldfind
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We consider non(anti)commutative (NAC) deformations of d=1 N=2 superspace. We find that, in the chiral base, the deformation preserves only a half of the original (linearly realized) supercharge algebra, as it usually happens in NAC field theories. We obtain in terms of a real supermultiplet a closed expression for a deformed Quantum Mechanics Lagrangian in which the original superpotential is smeared, similarly to what happens for the two dimensional deformed sigma model. Quite unexpectedly, we find that a second conserved charge can be constructed which leads to a nonlinear field realization of the supersymmetry algebra, so that finally the deformed theory has as many conserved supercharges as the undeformed one. The quantum behavior of these supercharges is analyzed.

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