nForum - Discussion Feed (Wigner theorem) 2023-03-26T16:00:10+00:00 https://nforum.ncatlab.org/ Lussumo Vanilla & Feed Publisher Urs comments on "Wigner theorem" (100968) https://nforum.ncatlab.org/discussion/9917/?Focus=100968#Comment_100968 2022-07-13T17:43:34+00:00 2023-03-26T16:00:10+00:00 Urs https://nforum.ncatlab.org/account/4/ I have now expanded a fair bit, written out the actual statement (starting in a new section “Preliminaries” here) and also adding an “Idea”-section (here). diff, v13, current

I have now expanded a fair bit, written out the actual statement (starting in a new section “Preliminaries” here) and also adding an “Idea”-section (here).

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Urs comments on "Wigner theorem" (100965) https://nforum.ncatlab.org/discussion/9917/?Focus=100965#Comment_100965 2022-07-13T11:26:33+00:00 2023-03-26T16:00:10+00:00 Urs https://nforum.ncatlab.org/account/4/ The statement in the entry was missing the condition that the map sends lines to lines, i.e. that it is a map of projective spaces. I have made a quick edit, but no time for more for the moment.

The statement in the entry was missing the condition that the map sends lines to lines, i.e. that it is a map of projective spaces. I have made a quick edit, but no time for more for the moment.

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Miklós comments on "Wigner theorem" (100961) https://nforum.ncatlab.org/discussion/9917/?Focus=100961#Comment_100961 2022-07-13T07:45:47+00:00 2023-03-26T16:00:10+00:00 Miklós https://nforum.ncatlab.org/account/1148/ Is this theorem true at all? Let the function ff map (z 1,z 2,&hellip;)(z_1,z_2,\dots) to (z¯ 1,z 2,&hellip;)(\overline z_1, z_2,\dots) where the coordinates refer to a Hilbert basis. This ...

Is this theorem true at all? Let the function $f$ map $(z_1,z_2,\dots)$ to $(\overline z_1, z_2,\dots)$ where the coordinates refer to a Hilbert basis. This is a surjective norm-preserving transformation but isn’t unitary or anti-unitary even up to phase.

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Miklós comments on "Wigner theorem" (96792) https://nforum.ncatlab.org/discussion/9917/?Focus=96792#Comment_96792 2021-11-28T09:38:36+00:00 2023-03-26T16:00:10+00:00 Miklós https://nforum.ncatlab.org/account/1148/ There is a minor inaccuracy in the statment, since anti-unitary operators are not linear (they are anti-linear). There is a minor inaccuracy in the statment, since anti-unitary operators are not linear (they are anti-linear). ]]> Miklós comments on "Wigner theorem" (87709) https://nforum.ncatlab.org/discussion/9917/?Focus=87709#Comment_87709 2020-11-14T07:50:29+00:00 2023-03-26T16:00:10+00:00 Miklós https://nforum.ncatlab.org/account/1148/ .

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Urs comments on "Wigner theorem" (78002) https://nforum.ncatlab.org/discussion/9917/?Focus=78002#Comment_78002 2019-05-14T09:36:06+00:00 2023-03-26T16:00:10+00:00 Urs https://nforum.ncatlab.org/account/4/ and added this one (thanks to David R.): C. S. Sharma and D. F. Almeida, Additive isometries on a quaternionic Hilbert space, Journal of Mathematical Physics 31, 1035 (1990) ...

and added this one (thanks to David R.):

• C. S. Sharma and D. F. Almeida, Additive isometries on a quaternionic Hilbert space, Journal of Mathematical Physics 31, 1035 (1990) (doi:10.1063/1.528779)
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Urs comments on "Wigner theorem" (78001) https://nforum.ncatlab.org/discussion/9917/?Focus=78001#Comment_78001 2019-05-14T09:30:28+00:00 2023-03-26T16:00:10+00:00 Urs https://nforum.ncatlab.org/account/4/ added pointer to Valentine Bargman, Note on Wigner’s theorem on symmetry transformations, Journal of Mathematical Physics 5.7 (1964): 862-868 (doi:10.1063/1.1704188) diff, v8, current