Monopole ’83 pp 223-228 | Cite as

# A Friedel Sum Rule for the Dyon Charge

Chapter

## Abstract

In understanding the ground state of the magnetic monopole, insight can be gained by regarding the magnetic monopole as an impurity in the Dirac sea, much as solid-state theorists investigate magnetic impurities in the Fermi sea. The angle θ that measures the amount of CP violation in the theory can be regarded as a probe of the ground, much as solid-state physicists use an external magnetic field to probe the Fermi sea. In a CP violating theory, the magnetic monopole acquires a non-zero electric charge that does not violate any quantization condition.
can be thought of as arising from a polarization of the ground state of the magnetic monopole by the CP violating term \(
\theta \vec E\cdot\vec B.
\)
A connection can be made with the Friedel Sum Rule that solid state physicists use. This determines the polarization charge, Z, in terms of the scattering phase shift, δ, of condition band electrons at the Fermi level off the impurity

^{1,2,3}The value of this charge$$
Q = - \frac{{e\theta }}
{{2\pi }}
$$

$$
Z = \frac{2}
{\pi }\Sigma _\ell \left( {2\ell + 1} \right)\delta _\ell \left( {E_F } \right).
$$

## Keywords

Magnetic Impurity Magnetic Monopole Scatter Phase Shift Chiral Angle Negative Energy State
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## Copyright information

© Plenum Press, New York 1984