A note on anomalous Jacobians in 2+1 dimensions

TL;DR

This paper investigates how local redefinitions of fermionic fields in massless QED3 induce anomalous Jacobians that modify the effective action, revealing insights into the structure of quantum anomalies and their impact on the theory.

Contribution

It demonstrates that the anomalous Jacobian and additional terms from field redefinitions precisely reproduce the quadratic term in the effective action of massless QED3.

Findings

The Jacobian contributes a quadratic parity-conserving term.

New terms from Dirac operator modifications are significant.

Finite decoupling transformations are unlikely to simplify non-perturbative analysis.

Abstract

There exist local infinitesimal redefinitions of the fermionic fields, which may be used to modify the strength of the coupling for the interaction term in massless QED3. Under those (formally unitary) transformations, the functional integration measure changes by an anomalous Jacobian, which (after regularization) yields a term with the same structure as the quadratic parity-conserving term in the effective action. Besides, the Dirac operator is affected by the introduction of new terms, apart from the modification in the minimal coupling term. We show that the result coming from the Jacobian, plus the effect of those new terms, add up to reproduce the exact quadratic term in the effective action. Finally, we also write down the form a finite decoupling transformation would have, and comment on the unlikelihood of that transformation to yield a helpful answer to the non-perturbative evaluation of the fermionic determinant.