Chirality Production with Mass Effects-Schwinger Pair Production and the Axial Ward Identity

TL;DR

This paper reviews how mass effects influence chirality production through the axial Ward identity and Schwinger pair production, contrasting equilibrium and out-of-equilibrium scenarios and their impact on the chiral anomaly.

Contribution

It provides a detailed analysis of the role of vacuum states and formalism choices in predicting chiral anomaly behavior in electromagnetic backgrounds.

Findings

In-out formalism predicts vanishing chiral anomaly in equilibrium.

In-in formalism captures out-of-equilibrium effects and particle pair production.

Mass suppression affects the out-of-equilibrium chiral anomaly.

Abstract

The anomalous generation of chirality with mass effects via the axial Ward identity and its dependence on the Schwinger mechanism is reviewed, utilizing parity violating homogeneous electromagnetic background fields. The role vacuum asymptotic states play on the interpretation of expectation values is examined. It is discussed that observables calculated with an in-out scattering matrix element predict a scenario under Euclidean equilibrium. A notable ramification of which is a vanishing of the chiral anomaly. In contrast, it is discussed observables calculated under an in-in, or real-time, formalism predict a scenario out-of equilibrium, and capture effects of mean produced particle anti-particle pairs due to the Schwinger mechanism. The out-of equilibrium chiral anomaly is supplemented with exponential quadratic mass suppression as anticipated for the Schwinger mechanism. Similar behavior in and out-of equilibrium is reviewed for applications including the chiral magnetic effect and chiral condensate.