11 papers
The Exterior Calculus and Relativistic Quantum Mechanics
Jose G. Vargas
In 1960-62, E. Kähler developed what looks as a generalization of the exterior calculus, which he based on Clifford rather than exterior algebra. The role of\ the exterior derivati…
Geometric Unification in Classical Physics
Jose G. Vargas
We show that always present in the autoparallels, even in natural liftings to the Finsler bundle of arbitrary connections, the Lorentz force is inescapable in Finsler geometry. The…
Algebraic Quarks from the Tangent Bundle: Methodology
Jose G. Vargas
In a previous paper, we developed a table of components of algebraic solutions of a system of equations generated by an inhomogeneous proper-value equation involving Kähler's total…
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 Units Imaginary in Kaehler's Quantum Mechanics
Jose G. Vargas
Inspired by a similar, more general treatment by Kahler, we obtain the spin operator by pulling to the Cartesian coordinate system the azimuthal partial derivative of differential…
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…
Opera's neutrinos and the Robertson test theory of the Lorentz transformations
Jose G. Vargas
The difference in light's travel time from CERN to GPS to Gran Sasso, on the one hand, and light going the direct route in vacuum (mimicked by neutrinos), on the other hand, is ana…