As further explained in ref. [1]:
“This (super) symmetry...(of the superspace)... can be realized on ordinary fields (that are defined as certain functions of physical spacetime(s)) by transformations that mix bosons and fermions. Such realizations suffice to study supersymmetry (one can write invariant actions, etc.) but are as cumbersome and inconvenient as doing vector calculus component by component. A compact alternative to this `component field' approach is given by the superspace-superfield approach", which is defined next.
Remarks: Supersymmetry is expected to be manifested, or observable, in such superspaces, that is, the supersymmetry algebras are represented by translations and rotations involving both the spacetime and the anticommuting coordinates. Then, the transformations of the `component fields' can be computed from the Taylor expansion of the translated and rotated superfields. Especially important are those transformations that mix boson and fermion symmetries; further details are found in ref. [2].
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