2020/06/04 by Tamagni, Spencer, Efthimiou, Costas
#FOS: Physical sciences #General Physics (physics.gen-ph)
paper · doi:10.48550/arxiv.2006.07149
Using techniques from geometry and complex analysis in their simplest form, we present a derivation of electric fields on surfaces with non-trivial topology. A byproduct of this analysis is an intuitive visualization of elliptic functions when their argument is complex-valued. The underlying connections between these techniques and the theory of Riemann surfaces are also explained. Our goal is to provide students and instructors a quick reference article for an extraordinary topic that is not included in the standard books.