Lagrangian magnetic moment from polarization

TL;DR

This paper derives an effective Lagrangian for the electron magnetic moment using background field methods, Fierz transformations, and explores symmetries and a model for magnetic moment generation.

Contribution

It introduces a novel approach to calculate the effective Lagrangian for electromagnetic form factors, including a model for the electron magnetic moment at tree level.

Findings

Derived the effective Lagrangian for magnetic moments.

Identified approximate rotational chiral symmetry in interactions.

Proposed a model for tree-level magnetic moment production.

Abstract

An effective Lagrangian term for the electron magnetic moment, and more generally electromagnetic form factors, is calculated by considering the background field method. Two Fierz transformations are performed for a one-photon exchange interaction, and the ambiguity in doing such transformations is exploited. The resulting effective interaction may exhibit an approximated rotational chiral symmetry either for the scalar-pseudoscalar currents interaction or for the vector-axial currents interaction. The leading terms in the expansion of the fermion determinant yield the leading QED effective action with the complete one loop electromagnetic form factors. A model is proposed to produce the tree level magnetic moment term.