2021/10/31 by F. Escalante · 1 citation
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Arithmetic zeta function #Charge (physics) #Context (archaeology) #Electrostatics #Field (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Point particle #Prime zeta function #Pure mathematics #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications #Quantum mechanics #Regularization (linguistics) #Riemann zeta function #Statistical physics #Zeta function regularization #Zeta potential #physics.class-ph
paper · pdf · doi:10.1088/1361-6404/ac5915
published in European Journal of Physics 43(3), 035810 (IOP Publishing) · 10 pages, 2 figures
openalex publication_date 2022/02/28 · arxiv created 2022/03/03 · arxiv updated 2022/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Spectral functions, such as the zeta functions, are widely used in Quantum Field Theory to calculate physical quantities. In this work, we compute the electrostatic potential and field due to an infinite discrete distribution of point charges, using the zeta function regularization technique. This method allows us to remove the infinities that appear in the resulting expression. We found that the asymptotic behavior dependence of the potential and field is similar to the cases of continuous charge distribution. Finally, this exercise can be useful for graduate students to explore spectral and special functions.