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

## TL;DR

This paper demonstrates that an unpolarized proton in a uniform, time-varying magnetic field acquires a Casimir momentum due to electroweak self-interaction, linking quantum vacuum effects to particle energy.

## Contribution

It extends previous work on chiral molecules to fundamental particles, showing that EW interactions induce measurable momentum transfer in magnetic fields.

## Key findings

- Proton gains kinetic momentum antiparallel to magnetic field.
- Virtual leptons acquire opposite Casimir momentum.
- Proton's kinetic energy is part of its electroweak self-energy.

## Abstract

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 Fermi's constant. We prove that the kinetic energy of the proton is a magnetic energy which forms part of its EW self-energy.