2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/187319Various forms of the $q$-boson are explained and their hidden symmetry revealed by transformations using the exponential phase operator. Both the one-component and the multicomponent $q$-bosons are discussed. As a byproduct, we obtain a new boson algebra having a shifted vacuum structure and define a global operatal $U(1)$ gauge transformation.18 pages, LaTex(run twice), To appear in J. PHys. AQuantum AlgebraHigh Energy Physics - Theorytext