Axial Anomaly, entanglement and polarization

Abstract

The (pion) decays controlled by axial anomaly imply the specific entanglement between photons having also the counterparts for classical electromagnetic waves. This is also a specific case of Eisnstein-Podolsky-Rosen-Bohm-Aharonov effect. The absence of causality and non-locality in (angular) momentum conservation is manifested, being especially clear for the generalization to the case of time rather than space separation corresponds to the polarization of dileptons described by time-like pion transition formfactors which may be studied experimentally. The similar decays in external magnetic field manifest the interplay with vacuum conductivity in external magnetic field and longitudinal polarization of vector mesons observed in heavy-ion collisions.