2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/54049We investigate the consistency of the background-field formalism when applying various regularizations and renormalization schemes. By an example of a two-dimensional $σ$ model it is demonstrated that the background-field method gives incorrect results when the regularization (and/or renormalization) is noninvariant. In particular, it is found that the cut-off regularization and the differential renormalization belong to this class and are incompatible with the background-field method in theories with nonlinear symmetries.12 pages, LATEXHigh Energy Physics - Theorytext