Summary
It is shown that, apart from arbitrary point transformations, only linear transformations are allowed in the functional space. In particular, it is not possible to construct a Riemannian geometry in the functional space considered here.
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References
Dirac, P. A. M.The Principles of Quantum Mechanics (Oxford: Clarenden Press), 1947.
VachaspatiMat. Fys. Medd. Dan. Vid. Selsk., 1956,30, No. 21.
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(Communicated by Dr. B. S. Madhava Rao,f.a.sc.)
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Vachaspati Transformations in the functional space of quantum mechanics. Proc. Indian Acad. Sci. 47, 179–183 (1958). https://doi.org/10.1007/BF03052637
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DOI: https://doi.org/10.1007/BF03052637