[Paper Review] Towards an Effective Field Theory of QED

Jerzy Kijowski, Gerd Rudolph+1 more|ArXiv.org|Sep 16, 1999

Black Holes and Theoretical Physics4 references3 citations

TL;DR

This paper proposes a novel effective field theory formulation of Quantum Electrodynamics (QED) by reducing the functional integral to gauge-invariant bosonic fields through an averaging procedure, enabling tractable calculations. It successfully computes the current-current propagator and the chiral anomaly within this new framework, demonstrating its viability for studying gauge theories with fermions via local gauge 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.

Motivation & Objective

• To develop a tractable effective field theory for QED by eliminating fermionic degrees of freedom through gauge-invariant field redefinition.
• To address the challenge of quantizing gauge theories with fermions by focusing on local gauge invariants rather than gauge-dependent fields.
• To provide a systematic framework for computing physical observables like the current-current propagator and the chiral anomaly in a gauge-invariant manner.
• To establish a foundation for analyzing non-Abelian gauge theories with fermions using similar invariant-based field redefinitions.

Proposed method

• Reduction of the QED functional integral to an integral over bosonic, gauge-invariant fields using a field redefinition that eliminates fermionic degrees of freedom.
• Application of a specific averaging method to the reduced functional integral to obtain a well-defined effective quantum field theory.
• Use of the resulting effective action to compute correlation functions, particularly the current-current propagator.
• Derivation of the chiral anomaly using the effective theory, ensuring gauge invariance and consistency with known anomalies.
• Adoption of a formalism that treats fermions implicitly through their gauge-invariant combinations, avoiding direct quantization of fermionic fields.
• Employment of standard techniques in effective field theory to extract physical observables from the averaged, gauge-invariant formulation.

Experimental results

Research questions

• RQ1 Can the functional integral of QED be consistently reduced to an integral over gauge-invariant bosonic fields?
• RQ2 Does the proposed averaging procedure yield a tractable and physically meaningful effective quantum field theory?
• RQ3 Can the current-current propagator be accurately computed in this new effective field theory formulation?
• RQ4 Is the chiral anomaly correctly reproduced within this gauge-invariant effective field theory framework?
• RQ5 Can this method be generalized to other gauge theories with fermions?

Key findings

• The functional integral of QED is successfully reduced to an integral over gauge-invariant bosonic fields, eliminating explicit fermionic degrees of freedom.
• The proposed averaging method yields a well-defined effective quantum field theory that is amenable to perturbative calculations.
• The current-current propagator is computed within the new formulation and shown to be consistent with standard QED results.
• The chiral anomaly is derived in the effective theory, confirming its correct structure and gauge-invariant origin.
• The method provides a consistent framework for analyzing gauge theories with fermions through local gauge invariants, avoiding gauge-fixing ambiguities.