Quantum Mechanics in Non(Anti)Commutative Superspace
arXiv:hep-th/0604197 · doi:10.1088/1126-6708/2006/08/081
Abstract
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.
13 pages
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