6 papers · 1 filter
Total Operators and Inhomogeneous Proper Values Equations
Jose G. Vargas
Kaehler's two-sided angular momentum operator, K + 1, is neither vector-valued nor bivector-valued. It is total in the sense that it involves terms for all three dimensions. Consta…
Kaehler Algebra: Idempotents for Solutions with Symmetry in Metric Spaces
Jose G. Vargas
With his Clifford algebra of differential forms, Kaehler's algebra addresses the overlooked manifestation of symmetry in the solutions of exterior systems. In this algebra, solutio…
Helmholtz-Hodge Theorems: Unification of Integration and Decomposition Perspectives
Jose G. Vargas
We develop a Helmholtz-like theorem for differential forms in Euclidean space using a uniqueness theorem similar to the one for vector fields. We then apply it to Riemannia…
Helmholtz Theorem for Differential Forms in 3-D Euclidean Space
Jose G. Vargas
There are significant differences between Helmholtz and Hodge's decomposition theorems, but both share a common flavor. This paper is a first step to bring them together. We here p…
Real Version of Calculus of Complex Variable (I): Weierstrass Point of View
Jose G. Vargas
A very small amount of Kähler algebra (i.e. Clifford algebra of differential forms) in the real plane makes x + ydxdy emerge as a factor between the differentials of the Cartesian…
Real Version of Calculus of Complex Variable (II): Cauchy's Point of View
Jose G. Vargas
As was the case in a previous paper, the differential form x+ydxdy plays the role that the variable z plays in the standard calculus of complex variable. The role of holomorphic fu…