Towards an Effective Field Theory of QED

TL;DR

This paper introduces a new approach to quantum electrodynamics (QED) by reformulating it in terms of gauge-invariant bosonic fields, enabling more tractable calculations of key phenomena like the current-current propagator and chiral anomaly.

Contribution

It presents a novel method for reducing the QED functional integral to gauge-invariant bosonic fields and proposes an averaging technique to develop an effective quantum field theory.

Findings

Calculated the current-current propagator within the new formulation

Derived the chiral anomaly using the gauge-invariant approach

Provided a framework for analyzing gauge theories with fermions in terms of local invariants

Abstract

A procedure for reducing the functional integral of QED to an integral over bosonic gauge invariant fields is presented. Next, a certain averaging method for this integral, giving a tractable effective quantum field theory, is proposed. Finally, the current-current propagator and the chiral anomaly are calculated within this new formulation. These results are part of our programme of analyzing gauge theories with fermions in terms of local gauge invariants.