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

TL;DR

This paper explores how Lowenstein-Zimmermann mass terms naturally emerge in massless QED in 2+1 dimensions through a field-dependent BRST transformation, linking renormalization techniques with symmetry transformations.

Contribution

It demonstrates that Lowenstein-Zimmermann mass terms arise naturally via a finite field-dependent BRST transformation in massless QED3, connecting renormalization and symmetry methods.

Findings

Lowenstein-Zimmermann mass terms appear naturally through FFBRST transformations.

The study extends BRST symmetry to include Nielsen identities.

The work links renormalization parameters with symmetry transformations.

Abstract

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.