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        "quote": "where the phase $\\varphi$ may depend on $g$ and $h$. This is called a <u class=\"concept-term\" data-concept-identity=\"urn:uuid:f737cbbc-e965-4626-9dda-4d856c66b811\" data-concept-route=\"/concept-identities#concept-f737cbbc-e965-4626-9dda-4d856c66b811\" id=\"first-de8e2adf86ce24a42446-en\">projective</u> or ray representation of the group $G$ on the Hilbert space . It is not in general possible to choose the phases such that all $\\mathrm { e } ^ { i \\varphi } = 1$ , giving a genuine representation. For a continuous group (see <a href=\"../chapter-10/08-topological-groups#section-10-8\" class=\"cross-reference\" id=\"xref-03-symmetry-transformations-5\" data-reference=\"section-10-8\">Section 10.8</a>), elements in the component of the identity $G _ { 0 }$ must be unitary since they are connected continuously with the identity element, which is definitely unitary. Anti-unitary transfor mations can only correspond to group elements in components that are not continuously connected with the identity.",
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