Abstract
Following the construction of tensor product spaces of quaternion Hilbert modules in our previous paper, we define the analogue of a ray (in a complex quantum mechanics) and the corresponding projection operator, and through these the notion of a state and density operators. We find that there is a one-to-one correspondence between a state and an equivalence class of vectors from the tensor product space, which gives us another method to define the gauge transformations.
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On sabbatical leave from the School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel. Work supported in part by a fellowship from the Ambrose Monell Foundation.
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Razon, A., Horwitz, L.P. Projection operators and states in the tensor product of quaternion hilbert modules. Acta Appl Math 24, 179–194 (1991). https://doi.org/10.1007/BF00046891
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DOI: https://doi.org/10.1007/BF00046891