  In this paper we use the notion of slice monogenic functions \cite{slicecss}
to define a new functional calculus for an $n$-tuple $T$ of not necessarily
commuting operators. This calculus is different from the one discussed in
\cite{jefferies} and it allows the explicit construction of the eigenvalue
equation for the $n$-tuple $T$ based on a new notion of spectrum for $T$. Our
functional calculus is consistent with the Riesz-Dunford calculus in the case
of a single operator.
