Expectation value of the axial-vector current in the external electromagnetic field

TL;DR

This paper calculates the expectation value of the axial-vector current in a constant external electromagnetic field using Schwinger's proper time method, revealing a Lorentz-invariant form of the effective Lagrangian.

Contribution

It provides a new calculation of the axial-vector current expectation value in electromagnetic fields, including anomaly and Lorentz-invariant terms, using a specific method.

Findings

Effective Lagrangian is Lorentz invariant.

Includes anomaly and additional Lorentz-invariant terms.

Results compare with previous photon-Z boson mixing calculations.

Abstract

We are calculated the expectation value of the axial-vector current induced by the vacuum polarization effect of the Dirac field in constant external electromagnetic field. In calculations we use Schwinger's proper time method. The effective Lagrangian has very simple Lorenz invariant form. Along with the anomaly term, it also contains two Lorenz invariant terms. The result is compared with our previous calculation of the photon - Z boson mixing in the magnetic field.