Non-perturbative Euler-Heisenberg Lagrangian and Paraelectricity in Magnetized Massless QED

TL;DR

This paper calculates a non-perturbative Euler-Heisenberg Lagrangian for massless QED in strong magnetic fields, revealing significant paraelectricity due to magnetic catalysis of chiral symmetry breaking, with potential experimental implications.

Contribution

It introduces a non-perturbative approach to the Euler-Heisenberg Lagrangian in massless QED under strong magnetic fields, highlighting the role of magnetic catalysis and infrared contributions.

Findings

System exhibits strong paraelectricity parallel to magnetic field.

Electric susceptibility depends non-analytically on fine-structure constant.

Large electric susceptibility linked to chiral condensate orientation.

Abstract

In this paper we calculate the non-perturbative Euler-Heisenberg Lagrangian for massless QED in a strong magnetic field $H$, where the breaking of the chiral symmetry is dynamically catalyzed by the external magnetic field via the formation of an electro-positron condensate. This chiral condensate leads to the generation of dynamical parameters that have to be found as solutions of non-perturbative Schwinger-Dyson equations. Since the electron-positron pairing mechanism leading to the breaking of the chiral symmetry is mainly dominated by the contributions from the infrared region of momenta much smaller than $\sqrt{eH}$, the magnetic field introduces a dynamical ultraviolet cutoff in the theory that also enters in the non-perturbative Euler-Heisenberg action. Using this action, we show that the system exhibits a significant paraelectricity in the direction parallel to the magnetic field. The nonperturbative nature of this effect is reflected in the non-analytic dependence of the obtained electric susceptibility on the fine-structure constant. The strong paraelectricity in the field direction is linked to the orientation of the electric dipole moments of the pairs that form the chiral condensate. The large electric susceptibility can be used to detect the realization of the magnetic catalysis of chiral symmetry breaking in physical systems.