Notes on Magnetic Monopoles from Partial Electromagnetic Duality

In this work, we propose a novel partial electromagnetic duality and construct its consistent realization using an extended gauge group $\mathrm{U}(1)_{\mathrm{q}}^{}\otimes\mathrm{U}(1)_{\mathrm{d}}^{}$ over a localized space region, where $\mathrm{U}(1)_{\mathrm{q}}^{}$ is the conventional gauge group of QED and $\mathrm{U}(1)_{\mathrm{d}}^{}$ serves as its dual gauge group. In this framework, the "electric" charge associated with $\mathrm{U}(1)_{\mathrm{d}}^{}$ plays the role of the magnetic (monopole) charge in QED $\mathrm{U}(1)_{\mathrm{q}}^{}$, whereas the electric charge of $\mathrm{U}(1)_{\mathrm{q}}^{}$ is reinterpreted as the "magnetic" charge of $\mathrm{U}(1)_{\mathrm{d}}^{}$. Importantly, our theory preserves the exact Bianchi identity, as it provides a genuinely singularity-free and stringless formulation that involves only electric charges under each U(1) gauge group. We show that the two gauge sectors, $\mathrm{U}(1)_{\mathrm{q}}^{}$ and $\mathrm{U}(1)_{\mathrm{d}}^{}$, exhibit a partial duality within a localized region of space. Based on this consistent formulation, we present the first fully gauge-invariant computation of scattering amplitudes and cross sections for monopole production processes, including $\mathrm{e}^-\mathrm{e}^+\rightarrow\chi\chi^*$ and $\mathrm{e}^-\mathrm{e}^+\rightarrow\chi\bar{\chi}$.