Abstract
The N=4 extended supersymmetry in four-dimensional space-time is considered from the viewpoint of the two included N=2 extended supersymmetries. Using the results for the structure of the irreducible superfields in N=2 superspace obtained earlier the task of explicit construction of N=4 irreducible superfields with SU(2)×SU(2) internal symmetry in N=2×2 superspace is solved. The decomposition of the N=4 scalar superfield into N=4 irreducible ones is described and the rules for collecting the irreducible scalar N=2×2 superfields with SU(2)×SU(2) internal symmetry into N=4 irreducible scalar superfields with SU(4) internal symmetry are set. To illustrate this method a simple consistent way of constructing the linearized off-shell N=4 conformal supergravity in N=4 superspace is shown.
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