Abstract
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 \(\mathbb {R}^n\).
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Acknowledgements
We would like to thank Brian Hall for his valuable suggestions and also to the anonymous reviewers for helpful comments. This work was partially supported by the Development and Promotion of Science and Technology Talents Project.
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Communicated by Hendrik De Bie.
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Eaknipitsari, S., Lewkeeratiyutkul, W. Clifford Algebra-Valued Segal–Bargmann Transform and Taylor Isomorphism. Adv. Appl. Clifford Algebras 31, 68 (2021). https://doi.org/10.1007/s00006-021-01171-2
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DOI: https://doi.org/10.1007/s00006-021-01171-2