It is a long-standing non-trivial prediction of quantum electrodynamics that its vacuum is unstable in the background of a static, spatially uniform electric field and, in principle, sparks with spontaneous emission of electron-positron pairs. However, an experimental verification of this prediction seems out of reach because a sizeable rate for spontaneous pair production requires an extraordinarily strong electric field strength |E| of order the Schwinger critical field, Ec = m 2 e /e 1.3×10 18 V/m, where me is the electron mass and e is its charge. Here, we show that the measurement of the rate of pair production due to the decays of high-energy bremsstrahlung photons in a high-intensity laser field allows for the experimental determination of the Schwinger critical field and thus the boiling point of the vacuum of quantum electrodynamics.

The dynamics of an anapole seen as dark matter at low energies is studied by solving the Schrödinger-Pauli equation in a potential involving Dirac-delta and its derivatives in threedimensions. This is an interesting mathematical problem that, as far as we know, has not been previously discussed. We show how bound states emerge in this approach and the scattering problem is formulated (and solved) directly. The total cross section is in full agreement with independent calculations in the standard model.

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We consider a model of dark quantum electrodynamics which is coupled to a visible photon through a kinetic mixing term. We compute the gχ − 2 for the dark fermion, where gχ is its gyromagnetic factor. We show that the gχ − 2 of the dark fermion is related to the g χ − 2 of (visible) quantum electrodynamics through a constant which depends on the kinetic mixing factor. We determine gχ − 2 as a function of the mass ratio κ = mB/mχ where mB and mχ denote the masses of the dark photon and the dark fermion respectively and we show how gχ − 2 become very different for light and heavy fermions around mB ≤ 10 −4 eV. * Electronic address: das@pas.rochester.edu †