Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-09-30
Int.J.Mod.Phys. A18 (2003) 855-878
Physics
High Energy Physics
High Energy Physics - Theory
30 pages, Latex, no figures, some modifications including change of notations and addition of some comments
Scientific paper
10.1142/S0217751X03012333
Based on an argument for the noncommutativity of momenta in noncommutative directions, we arrive at a generalization of the ${\cal N}=1$ super $E^2$ algebra associated to the deformation of translations in a noncommutative Euclidean plane. The algebra is obtained using appropriate representaions of its generators on the space of superfields in a $D=2, {\cal N}=1$ ``noncommutative superspace.'' We find that the (anti)commutators between several (super)translation generators are no longer vanishing, but involve a new set of generators which together with the (super)translation and rotation generators form a consistent closed algebra. We then analyze the spectrum of this algebra in order to obtain its fundamental and adjoint representations.
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