Abstract
It is well known that not every symmetry of a classical field theory is also a symmetry of its quantum version. When this occurs, we speak of quantum anomalies. The existence of anomalies imply that some classical Noether charges are no longer conserved in the quantum theory. In this paper, we discuss a new example for quantum electromagnetic fields propagating in the presence of gravity. We argue that the symmetry under electric-magnetic duality rotations of the source-free Maxwell action is anomalous in curved spacetimes. The classical Noether charge associated with these transformations accounts for the net circular polarization or the optical helicity of the electromagnetic field. Therefore, our results describe the way the spacetime curvature changes the helicity of photons and opens the possibility of extracting information from strong gravitational fields through the observation of the polarization of photons. We also argue that the physical consequences of this anomaly can be understood in terms of the asymmetric quantum creation of photons by the gravitational field.
Highlights
Symmetries are at the core of well-established physical theories, and they keep playing a central role in the mainstream of current research
When the symmetries of free theories are preserved by interactions, the conservation laws are maintained, and they can be used to understand patterns in diverse physical phenomena
For instance, the phase invariance is preserved by the coupling of the Dirac and the electromagnetic field, and this ensures the conservation of the net fermion number in all physical processes [1]
Summary
Symmetries are at the core of well-established physical theories, and they keep playing a central role in the mainstream of current research. For instance, the phase invariance is preserved by the coupling of the Dirac and the electromagnetic field, and this ensures the conservation of the net fermion number in all physical processes [1] Another illustrative example is the gravitationally induced creation of particles, either bosons or fermions, in an expanding homogenous universe [2,3,4,5]. As first proved in [15], these transformations leave the action of electrodynamics invariant if sources (charges and currents) are not present, and the associated Noether charge is precisely the difference between the intensity of the right- and left-handed circularly polarized electromagnetic waves, i.e., the net helicity This symmetry is exact in the classical theory even in the presence of an arbitrary gravitational background, as pointed out some years later in [16]. We will provide a general overview of these results from a different perspective, and with more emphasis on conceptual aspects
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