In this article one follows the model in which the origin of pseudogap is a consequence of massive gauge bosons with the mass acquisition a result of Stueckelberg mechanism. The effective gauge actions of this model is evaluated as well as the gauge field propagators in the symmetry breaking phase in which fermions are gapless and gapped. The article further generalizes the initial model to include electromagnetic interactions and discusses the effective interaction between the electromagnetic fields and the gauge bosons that are responsible for pseudogap formation. Particularly the dynamics of the gauge bosons in case of c-axis constant external magnetic field is evaluated and compared with relevant experiments such that the conclusion of a field-independent pseudogap is yielded.