  Classical Segal-Bargmann theory studies three Hilbert space unitary
isomorphisms that describe the wave-particle duality and the configuration
space-phase space. In this work, we generalized these concepts to Clifford
algebra-valued functions. We establish the unitary isomorphisms among the space
of Clifford algebra-valued square-integrable functions on $\mathbb{R}^n$ with
respect to a Gaussian measure, the space of monogenic square-integrable
functions on $\mathbb{R}^{n+1}$ with respect to another Gaussian measure and
the space of Clifford algebra-valued linear functionals on symmetric tensor
elements of $\mathbb{R}^n$.
