Single State Supermultiplet in 1+1 Dimensions

We discuss the issue of multiplicity of the BPS states in (1+1)-dimensional models with minimal N=1 supersymmetry. The previous argument that the irreducible representation of supersymmetry algebra is one-dimensional in this case is elaborated. Algebraic treatment is illustrated by explicit quasiclassical quantization in various weakly coupled models which present examples of oneand two-dimensional representations. For non-BPS multiplets, which are two-dimensional, one can introduce an operator of the fermion charge which differentiates between two distinct states in the multiplet. This operator is not defined for BPS states.