Acceleration of an unpolarized proton along a uniform magnetic field: Casimir momentum of leptons

It has been recently shown that a chiral molecule accelerates linearly along a spatially uniform magnetic field, as a result of the parity-time symmetry breaking induced in its QED self-interaction. In this work we extend this result to fundamental particles which present EW self-interaction, in which case parity is violated by the EW interaction itself. In particular, we demonstrate that, in a spatially uniform and adiabatically time-varying magnetic field, an unpolarized proton coupled to the leptonic vacuum acquires a kinetic momentum antiparallel to the magnetic field, whereas virtual leptons gain an equivalent $Casimir$ $momentum$ in the opposite direction. That momentum is proportional to the magnetic field and to the square of Fermis constant. We prove that the kinetic energy of the proton is a magnetic energy which forms part of its EW self-energy.