Mark Pankov: Wigner's theorem and its generalizations
Source: Algebra and functional analysis seminar
Roman Drnovšek in Primož Moravec
ABSTRACT: Let $H$ be a complex Hilbert space. The classical Wigner theorem can be formulated as follows: every bijective transformations of the set of pure states (i.e. $1$-dimensional subspaces of $H$) preserving the orthogonality relation in both directions is induced by a unitary or anti-unitary operator. There is also a non-bijective version of this result concerning transformations preserving the angles between pure states.
I describe some extensions of these results to Hilbert Grassmannians.