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.