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

Lewandowski, Adrian

doi:10.1016/j.nuclphysb.2018.08.004

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

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Lewandowski, Adrian
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Lewandowski, A. (2018). LSZ-reduction, resonances and non-diagonal propagators: gauge fields. Nuclear Physics B, 935, 40-82. doi:10.1016/j.nuclphysb.2018.08.004.

Cite as: https://hdl.handle.net/21.11116/0000-0002-74F8-4

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
$p^2$) 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
$Z^0$-photon mixing in the Standard Model and the $G_Z$-Majoron mixing in the
singlet Majoron model.