One-Parameter Subgroups of Unitary Groups with Indefinite Metric and in Particular of the Conformal Group

Abstract

Motivated by a problem concerning two‐variable expansions of covariant scattering amplitudes, and by recent theories involving indefinite metrics and the conformal group, we study subgroups of unitary groups with indefinite metric. The one‐parameter subgroup case reduces to finding canonical matrices for pseudo‐Hermitian operators with respect to orthonormal bases. By decomposing the space on which such operators act as far as possible as an orthogonal direct sum of invariant subspaces, one obtains invariant subspaces having indecomposable primary components. The general results, summarized in tables of canonical forms valid for any finite dimension, are supplemented by more detailed tables for low dimensions, including the case of the conformal group of space‐time.