Emergence of Lowenstein-Zimmermann mass terms for QED${}_3$

In this paper we consider a super-renormalizable theory of massless QED in $(2+1)$ dimensions and discuss their BRST symmetry transformation. By extending the BRST transformation we derive the Nielsen identities for the theory. Further, we compute the generalized BRST (so-called FFBRST) transformation by making the transformation parameter field-dependent. Remarkably, we observe that the Lowenstein-Zimmerman mass terms, containing Lowenstein-Zimmerman parameter which plays an important role in the BPHZL renormalization program, along with the external sources coupled to the non-linear BRST variations appear naturally in the theory through a FFBRST transformation.