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We propose a new lattice superfield formalism in momentum representationwhich accommodates species doublers of the lattice fermions and their bosoniccounterparts as super multiplets. We explicitly show that one dimensional N=2model with interactions has exact Lie algebraic supersymmetry on the latticefor all super charges. In coordinate representation the finite differenceoperator is made to satisfy Leibnitz rule by introducing a non local product,the ``star'' product, and the exact lattice supersymmetry is realized. Thestandard momentum conservation is replaced on the lattice by the conservationof the sine of the momentum, which plays a crucial role in the formulation.Half lattice spacing structure is essential for the one dimensional model andthe lattice supersymmetry transformation can be identified as a half latticespacing translation combined with alternating sign structure. Invariance underfinite translations and locality in the continuum limit are explicitlyinvestigated and shown to be recovered. Supersymmetric Ward identities areshown to be satisfied at one loop level. Lie algebraic lattice supersymmetryalgebra of this model suggests a close connection with Hopf algebraic exactnessof the link approach formulation of lattice supersymmetry.

Species Doublers as Super Multiplets in Lattice Supersymmetry: Exact Supersymmetry with Interactions for D=1 N=2