The Wigner-Bargmann theorem in the pseudo-unitary case
Let E be a complex vector space with an indefinite inner product, and \(\tilde E\) the corresponding projective space. The author considers the problem of lifting projective mappings \(T:\tilde E\to \tilde E\) to pseudo-unitary or anti-pseudo-unitary mappings \(U:E\to E.\) He proves that this can be done under natural conditions on T, thereby generalizing the classical result of Wigner for a definite inner product space. Similarly he considers the problem of lifting a projective representation on \(\tilde E\), of a Lie group G, to a pseudo-unitary or anti-pseudo-unitary representation on E. This can be done for a wide class of Lie groups and projective representations in the case that E is a J-space. This generalizes a result of Bargmann and extensions of it by Bracci, Morchie and Strocchi.
scientific article; zbMATH DE number 3863918