
Dual photon

In theoretical physics, the dual photon is a hypothetical elementary particle that is a dual of the photon under electric–magnetic duality which is predicted by some theoretical models, including M-theory.
It has been shown that including magnetic monopole in Maxwell's equations introduces a singularity. The only way to avoid the singularity is to include a second four-vector potential, called dual photon, in addition to the usual four-vector potential, photon. Additionally, it is found that the standard Lagrangian of electromagnetism is not dual symmetric (i.e. symmetric under rotation between electric and magnetic charges) which causes problems for the energy–momentum, spin, and orbital angular momentum tensors. To resolve this issue, a dual symmetric Lagrangian of electromagnetism has been proposed, which has a self-consistent separation of the spin and orbital degrees of freedom. The Poincaré symmetries imply that the dual electromagnetism naturally makes self-consistent conservation laws.
Dual electromagnetism.
The free electromagnetic field is described by a covariant antisymmetric tensor formula_1 of rank 2 by
where formula_3 is the electromagnetic potential.
The dual electromagnetic field formula_4 is defined as
where formula_6 denotes the Hodge dual, and formula_7 is the Levi-Civita tensor
For the electromagnetic field and its dual field, we have
Then, for a given gauge field formula_3, the dual configuration formula_11 is defined as 
where formula_11 the field potential of the dual photon, and non-locally linked to the original field potential formula_3.
"p"-form electrodynamics.
A "p"-form generalization of Maxwell's theory of electromagnetism is described by a gauge-invariant 2-form formula_16 defined as
which satisfies the equation of motion
where formula_6 is the Hodge star operator.
This implies the following action in the spacetime manifold formula_20:
where formula_22 is the dual of the gauge-invariant 2-form formula_16 for the electromagnetic field.
Dark photon.
The dark photon is a spin-1 boson associated with a U(1) gauge field, which could be massless and behaves like electromagnetism. But, it could be unstable and massive, quickly decays into electron–positron pairs, and interact with electrons.
The dark photon was first suggested in 2008 by Lotty Ackerman, Matthew R. Buckley, Sean M. Carroll, and Marc Kamionkowski to explain the "'g"–2 anomaly' in experiment E821 at Brookhaven National Laboratory. Nevertheless, it was ruled out in some experiments such as the PHENIX detector at the Relativistic Heavy Ion Collider at Brookhaven.
In 2015, the Hungarian Academy of Sciences's Institute for Nuclear Research in Debrecen, Hungary, suggested the existence of a new, light spin-1 boson, dubbed the X17 particle, 34 times heavier than the electron that decays into a pair of electron and positron with a combined energy of 17 MeV. In 2016, it was proposed that it is an X-boson with a mass of 16.7 MeV that explains the "g"−2 muon anomaly. 