Emergence of Lowenstein-Zimmermann mass terms for QED$_{3}$

Understand

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.