Z 2 n -graded extensions of supersymmetric quantum mechanics via Clifford algebras
N. Aizawa, K. Amakawa, S. Doi
Source abstract
It is shown that the N=1 supersymmetric quantum mechanics (SQM) can be extended to a Z2n-graded superalgebra. This is done by presenting quantum mechanical models that realize, with the aid of Clifford gamma matrices, the Z2n-graded Poincaré algebra in one-dimensional spacetime. Reflecting the fact that the Z2n-graded Poincaré algebra has a number of central elements, a sequence of models defining the Z2n-graded version of SQM is provided for a given value of n. In a model of the sequence, the central elements having the same Z2n-degree are realized as dependent or independent operators. It is observed that as the Clifford algebras of larger dimension are used, more central elements are realized as independent operators.
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