TITLE:
Inverse Differential Operators in Time and Space
AUTHORS:
Edwin Eugene Klingman
KEYWORDS:
Matrix-Inverse Differential Operators, Green’s Functions, Dirac’s Equation, Wave Equations, Inverse Curl Operator
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.11 No.12,
December
19,
2023
ABSTRACT: When one function is defined as a differential operation on another function, it’s often desirable to invert the definition, to effectively “undo” the differentiation. A Green’s function approach is often used to accomplish this, but variations on this theme exist, and we examine a few such variations. The mathematical analysis of is sought in the form if such an inverse operator exists, but physics is defined by both mathematical formula and ontological formalism, as I show for an example based on the Dirac equation. Finally, I contrast these “standard” approaches with a novel exact inverse operator for field equations.