Quantum-Electrodynamic Corrections to the Electron Charge Value in Metals

The quantum-electrodynamic renormalization of the electron's charge when in a metal (Fermi gas of electrons) environment is calculated. Solid-state many-body techniques are employed rather than the usual quantum-electrodynamic approach, so that the analogy to calculating a material's dielectric constant is exhibited. In metals, the renormalized charge value is increased over the vacuum value by $\frac{\delta e}{e}\cong 4\times {10}^{-10\mathrm{}}\rho$, where $\rho$ is the metal's electron density in $\frac{e}{\left({10}^{-24\mathrm{}}{\mathrm{cm}}^3\right)}$. These corrections are too small to affect the recent measurements of $\frac{e}{h}$ in metals using the Josephson frequency-voltage relation for superconducting junctions, which are accurate to ${10}^{-6\mathrm{}}$. Experiments to be done which will compare $\frac{e}{h}$ values in different metals to several orders of magnitude greater accuracy should detect the corrections to $e$ calculated in this paper.