An Invariance Property of the Free Electromagnetic Field

Abstract

In the absence of charges and currents, Maxwell's equations are invariant under the transformation E′ = E cosθ+B sinθ, B′ = −E sinθ+B cosθ. Using Noether's theorem, we show that the corresponding conserved quantity is proportional to the difference in the number of right and left circularly polarized photons in the field.

Electromagnetic Duality Anomaly in Curved Spacetimes

“…(27). Since in flat spacetime Q D represents the difference in number between photons of opposite helicity [8], this result can be interpreted as a nonconservation of the helicity of the quantum electromagnetic field in curved spacetimes.…”

“…[1] (see Ref. [8] for an earlier work), and the reader is referred to these references for details. At the level of the electromagnetic potential, duality rotations are implemented by the transformation δA µ = θ Z µ , with θ an infinitesimal parameter.…”

Optical helicity of interfering waves

“…It is this rotational symmetry that is associated with the conservation of the helicity of light, a connection made by Calkin [17] which ourselves and others have pursued elsewhere within the context of Noether's theorem [15,30]. There is thus a sense in which the optical helicity, H, embodies the principle of electric-magnetic democracy, a phrase coined by Berry [44].…”

“…We begin by recalling some observations regarding the helicity of light that have been made elsewhere by ourselves and others [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. The explicit expression for the total helicity of an optical field is…”

Duality and helicity: the photon wave function approach

“…In particular, the associated Noether quantity is the (optical) helicity [10], expressed as the integral of two Chern-Simons terms…”