# Axion-photon mixing in quantum field theory and vacuum energy

## TL;DR

This paper investigates axion-photon mixing within quantum field theory, revealing vacuum energy effects that resemble dark energy and suggesting potential experimental detection of axion-like particles through vacuum polarization phenomena.

## Contribution

It introduces a quantum field theory framework for axion-photon mixing, showing vacuum energy corrections and their cosmological implications, which were not previously analyzed in this context.

## Key findings

- Vacuum energy from axion-photon mixing mimics cosmological constant behavior.
- Corrections to oscillation formulas depend on magnetic field strength.
- Possible detection of vacuum polarization effects in laboratory experiments.

## Abstract

We analyze axion--photon mixing in the framework of quantum field theory. The condensate structure of the vacuum for mixed fields induces corrections to the oscillation formulae and leads to non-zero energy of the vacuum for the component of the photon mixed with the axion. This energy generates a new effect of the vacuum polarization and it has the state equation of the cosmological constant, $w = -1$. This result holds for any homogeneous and isotropic curved space-time, as well as for diagonal metrics. Numerical estimates of the corrections to the oscillation formulae are presented by considering the intensity of the magnetic field available in the laboratory. Moreover, we estimate the vacuum energy density induced by axion--photon mixing in the Minkowski space-time. A value compatible with that of the energy density of the universe can be obtained for axions with a mass of $(10^{-3}-10^{-2}) eV$ in the presence of the strong magnetic fields that characterize astrophysical objects such as pulsars or neutron stars. In addition, a value of the energy density less than that of the Casimir effect is obtained for magnetic fields used in experiments such as PVLAS. The vacuum polarization induced by this energy could be detected in next experiments and it might provide an indirect proof of the existence of the axion--photon mixing. The quantum field theory effects presented in this work may lead to new methods for studying axion-like particles.