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An Alternative Dimensional Reduction Prescription

We propose an alternative dimensional reduction prescription which in respect with Green functions corresponds to drop the extra spatial coordinate. From this, we construct the dimensionally reduced Lagrangians both for scalars and fermions, discussing bosonization and supersymmetry in the particular 2-dimensional case. We argue that our proposal is in some situations more physical, in the sense that it mantains the form of the interactions between particles, thus preserving the dynamics corresponding to the higher dimensional space.