Generalisations
In Clifford analysis, the operator D: C∞(Rk ⊗ Rn, S) → C∞(Rk ⊗ Rn, Ck ⊗ S) acting on spinor valued functions defined by
is sometimes called Dirac operator in k Clifford variables. In the notation, S is the space of spinors, are n-dimensional variables and is the Dirac operator in the i-th variable. This is a common generalization of the Dirac operator (k=1) and the Dolbeault operator (n=2, k arbitrary). It is an invariant differential operator, invariant under the action of the group SL(k) × Spin(n). The resolution of D is known only in some special cases.
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