LSZ-reduction, resonances and non-diagonal propagators: Gauge fields

We analyze in the Landau gauge mixing of bosonic fields in gauge theories with exact and spontaneously broken symmetries, extending to this case the Lehmann-Symanzik-Zimmermann (LSZ) formalism of the asymptotic fields. Factorization of residues of poles (at real and complex values of the variable p2) is demonstrated and a simple practical prescription for finding the “square-rooted” residues, necessary for calculating S-matrix elements, is given. The pseudo-Fock space of asymptotic (in the LSZ sense) states is explicitly constructed and its BRST-cohomological structure is elucidated. Usefulness of these general results, obtained by investigating the relevant set of Slavnov-Taylor identities, is illustrated on the one-loop examples of the Z0-photon mixing in the Standard Model and the GZ-Majoron mixing in the singlet Majoron model.