Bechluft-Sach, S. and Samion, E. (2019) Green’s Functions, Biot-Savart Operators, and Linking Numbers on Negatively Curved Symmetric Spaces. Journal of Mathematical Physics, 60, Article ID: 111503.
https://doi.org/10.1063/1.5109244

has been cited by the following article:

• TITLE: Exact Inverse Operator on Field Equations

  AUTHORS: Edwin Eugene Klingman

  KEYWORDS: Anti-Derivative, Anti-Curl Operator, Maxwell’s Equations, Geometric Calculus, Kasner Metric, Green’s Function, Biot-Savart Operator

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.8 No.10, October 27, 2020

  ABSTRACT: Differential equations of electromagnetic and similar physical fields are generally solved via antiderivative Green’s functions involving integration over a region and its boundary. Research on the Kasner metric reveals a variable boundary deemed inappropriate for standard anti-derivatives, suggesting the need for an alternative solution technique. In this work I derive such a solution and prove its existence, based on circulation equations in which the curl of the field is induced by source current density and possibly changes in associated fields. We present an anti-curl operator that is believed novel and we prove that it solves for the field without integration required.