𝒩 = 2 ℤ22-supersymmetry and quantum mechanics

In this short note, we briefly review the minimal [Formula: see text]-graded supersymmetric classical mechanics via superfield formalism and [Formula: see text] [Formula: see text]-graded quantum mechanics. In the classical mechanics, it is shown that [Formula: see text] [Formula: see text]-supersymmetric action was constructed by the similar way to the ordinary supersymmetry. The constructed Lagrangian is in two-dimensional because of the definition of the integration on minimal [Formula: see text]-superspace. After the dimensional reduction and quantization, we obtain [Formula: see text] [Formula: see text]-graded quantum mechanics which has different features from those introduced so far. It is a two-dimensional (two-particle) system and is the first example of the quantum mechanical realization of an eight-dimensional irrep of the [Formula: see text] [Formula: see text]-supersymmetry algebra.