Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 14th 2019

    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

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 14th 2019

    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)

    diff, v8, current

    • CommentRowNumber3.
    • CommentAuthorMiklós
    • CommentTimeNov 14th 2020
    • (edited Nov 14th 2020)

    .

    • CommentRowNumber4.
    • CommentAuthorMiklós
    • CommentTimeNov 28th 2021
    There is a minor inaccuracy in the statment, since anti-unitary operators are not linear (they are anti-linear).
    • CommentRowNumber5.
    • CommentAuthorMiklós
    • CommentTimeJul 13th 2022
    • (edited Jul 13th 2022)

    Is this theorem true at all? Let the function ff map (z 1,z 2,)(z_1,z_2,\dots) to (z¯ 1,z 2,)(\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.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJul 13th 2022

    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.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJul 13th 2022

    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