# Isospin precession in non-Abelian Aharonov-Bohm scattering

arxiv（2024）

Abstract

The concept of pseudoclassical isospin is illustrated by the non-Abelian
Aharonov-Bohm effect proposed by Wu and Yang in 1975. The spatial motion is
free however the isospin precesses when the enclosed magnetic flux and the
incoming particle's isosopin are not parallel. The non-Abelian phase factor
𝔉 of Wu and Yang acts on the isospin as an S-matrix. The
scattering becomes side-independent when the enclosed flux is quantized,
Φ_N=NΦ_0 with N an integer. The gauge group SU(2) is an internal
symmetry and generates conserved charges only when the flux is quantized, which
then splits into two series: for N=2k SU(2) acts trivially but for N=1+2k
the implementation is twisted. The orbital and the internal angular momenta are
separately conserved. The double rotational symmetry is broken to SO(2)×
SO(2) when N odd. For unquantized flux there are no internal symmetries, the
charge is not conserved and protons can be turned into neutrons.

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