We study a transform, inspired by coherent state transforms, from the Hilbert space of Clifford algebra valued square integrable functions L-2 (R-m, dx) circle times C-m to a Hilbert space of solutions of the Weyl equation on Rm+1 = R x R-m, namely, to the Hilbert space ML2 (Rm+1, d mu) of C-m-valued monogenic functions on Rm+1 which are L-2 with respect to an appropriate measure d mu. We prove that this transform is a unitary isomorphism of Hilbert spaces and that it is therefore an analog of the Segal-Bargmann transform for Clifford analysis. As a corollary, we obtain an orthonormal basis of monogenic functions on Rm+1. We also study the case when R-m is replaced by the m-torus T-m. Quantum mechanically, this extension establishes the unitary equivalence of the Schrodinger representation on M, for M = R-m and M = T-m, with a representation on the Hilbert space ML2 (R x M, d mu) of solutions of the Weyl equation on the space-time R x M. Published by AIP Publishing.