José Mourão, João P. Nunes, and Tao Qian, Coherent state transforms and the Weyl equation in Clifford analysis, Journal of Mathematical Physics, Volume 58, Issue 1, 10.1063/1.4974449, DOI: http://dx.doi.org/10.1063/1.4974449, Download: http://aip.scitation.org/doi/pdf/10.1063/1.4974449
Abstract: We study a transform, inspired by coherent state transforms, from the Hilbert space of Clifford algebra valued square integrable functions L2(ℝm, dx) ⊗ ℂm to a Hilbert space of solutions of the Weyl equation on ℝm+1 = ℝ × ℝm, namely, to the Hilbert space ℳL2(ℝm+1, dμ) of ℂm-valued monogenic functions on ℝm+1 which are L2 with respect to an appropriate measure dμ. 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 ℝm is replaced by the m-torus 𝕋m. Quantum mechanically, this extension establishes the unitary equivalence of the Schrödinger representation on M, for M = ℝm and M = 𝕋m, with a representation on the Hilbert space ℳL2(ℝ × M, dμ) of solutions of the Weyl equation on the space-time ℝ × M.
Source: Email from journals_AT_aip-info.org, 7th Feb. 2017