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§14.3 · en · original_transcription · unreviewed
where the phase may depend on and . This is called a projective or ray representation of the group on the Hilbert space . It is not in general possible to choose the phases such that all , giving a genuine representation. For a continuous group (see Section 10.8), elements in the component of the identity 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.