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

Abstract

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.