dyon

In physics, a dyon is a hypothetical particle with both electric and magnetic charges. A dyon with a zero electric charge is usually referred to as a monopole. Many Grand Unified Theories predict the existence of both monopoles and dyons.

Dyons in Dirac's theory

In Dirac's theory, a monopole is a point-like object which serves as a source of magnetic field. It is possible to consider a more complicated object which is a source of both electric and magnetic fields. Thus dyons are allowed, but not required by this theory. In quantum theory, the allowed values of the electric and magnetic charges are constrained by the Dirac-Zwanziger-Schwinger quantization condition: if there exists both a particle with electric charge

e_1

and magnetic charge

g_1

and a particle with electric charge

e_2

and magnetic charge

g_2

, then one must have

e_1 g_2-e_2 g_1=2\pi n c\hbar

, where

n

is an integer,

c

is the speed of light, and

\hbar

is the reduced Planck's constant. This condition follows from the requirement that the wavefunction describing the system of these two particles be univalued (more precisely, it should be a well-defined section of a suitable line bundle on the configuration space of the two particles).

Dyons in Grand Unified Theories

In Grand Unified Theories, dyons can be regarded as excited states of monopoles. More precisely, the classical monopole solution has a circle-valued degree of freedom whose semiclassical quantization leads to a tower of states of increasing electric charge. Thus Grand Unified Theories can be said to predict dyons. In particular, it is possible to predict the masses of dyons.

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