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

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### 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.

### Most cited references8

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### Author and article information

###### Journal
28 July 2019
###### Article
1907.13518

http://arxiv.org/licenses/nonexclusive-distrib/1.0/

###### Custom metadata
10-page main text, 7 appendices, 2 figures. This article partially supersedes arXiv:1810.12831
hep-ph hep-th quant-ph

Quantum physics & Field theory, High energy & Particle physics