Europhysics Letters (EPL)

The Wu-Yang Factor and the non-Abelian Aharonov-Bohm Experiment

P. A. Horváthy

Published Aug 1, 1986• 6 citations

Abstract

The scattering of nucleons on a non-Abelian flux is shown to depend, as predicted by Wu and Yang, on the nonintegrable phase factor.

DOI: 10.1209/0295-5075/2/3/005

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Europhysics Letters (EPL)

The Wu-Yang Factor and the non-Abelian Aharonov-Bohm Experiment

P. A. Horváthy

Published Aug 1, 1986• 6 citations

Publisher

Abstract

The scattering of nucleons on a non-Abelian flux is shown to depend, as predicted by Wu and Yang, on the nonintegrable phase factor.

DOI: 10.1209/0295-5075/2/3/005

Related papers

The non-Abelian Bohm-Aharonov effect in geometric quantisation

P. A. Horváthy, J. Kollár

The non-Abelian Bohm-Aharonov experiment proposed by Wu and Yang (1975) is studied in the geometric framework of Kostant (1970) and Souriau (1970).

Classical and Quantum GravityNov 11, 19846 citations

The non-Abelian Aharonov-Bohm effect

P. A. Horváthy

The scattering of a nucleon beam around a cylinder containing a non-Abelian flux is studied. We confirm all the previsions of Wu and Yang. We consider the generalization to the gauge group $SU(N)$ , and derive a classification scheme. Isospin precession is recovered also at the classical limit.The scattering of a nucleon beam around a cylinder containing a non-Abelian flux is studied. We confirm all the previsions of Wu and Yang. We consider the generalization to the gauge group $SU(N)$, and derive a classification scheme. Isospin precession is recovered also at the classical limit.

arXiv:2312.16133Dec 26, 20230 citations

Calculation of non-relativistic scattering of charged scalar particles from a classical Aharonov-Bohm solenoid without an explicit gauge choice

A. Y. Shiekh. Blackett Laboratory

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Isospin precession in non-Abelian Aharonov-Bohm scattering

Zhang, Peng-Ming, P. A. Horváthy

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 $\mathfrak{F}$ 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 $SO(2)\times SO(2)$ when $N$ odd. For unquantized flux there are no internal symmetries, the charge is not conserved and protons can be turned into neutrons.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 $\mathfrak{F}$ 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 $SO(2)\times SO(2)$ 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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The scattering of a nucleon beam around a cylinder containing a non-Abelian flux is studied. We confirm all the previsions of Wu and Yang. We consider the generalization to the gauge group

SU(N)

, and derive a classification scheme. Isospin precession is recovered also at the classical limit.

\mathfrak{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)\times 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.