Exact Inverse Operator on Field Equations

2023

JAMP

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The latter half of the twentieth century yielded two tools of unprecedented power, both of which took decades to mature to their current states. The purpose of this research is to apply these to a theory of gravity and develop the consequences of the model based on these tools. This paper presents such results without mathematical details, which are presented elsewhere. The tools are: Geometric Calculus, developed by David Hestenes, circa 1965 and Mathematica, released in 1988 by Steven Wolfram. Both tools have steep learning curves, requiring several years to acquire expertise in their use. This paper explains in what sense they are optimal.

“…A simpler solution to gravitomagnetic field equations is [6] the recently in-Journal of Applied Mathematics and Physics troduced inverse curl:…”

Section: Inverse Operations In Solving Equationsmentioning

confidence: 99%

Computational Physics of <i>Mathematica</i> and Geometric Calculus

2023

JAMP

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“…Recently an alternative technique of inverting field equations developed [8] based on exact discrete inverse operators. For magnetic field Equation 11describing the circulation of the field induced by current density j we use the discrete inverse curl operator…”

Section: Derivation Of Field Solution From Discrete Inverse Operatorsmentioning

confidence: 99%

A Self-Linking Field Formalism

2021

JMP

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The Gauss-linking integral for disjoint oriented smooth closed curves is derived linking integrals from the Biot-Savart description of the magnetic field. DeTurck and Gluck extend this linking from 3-space 3 R to () 2 SU space of the unit 3-sphere and hyperbolic space in Minkowski 1,3 R. I herein extend Gauss-linking to self-linking and develop the concept of self-dual, which is then applied to gravitomagnetic dynamics. My purpose is to redefine Wheeler's geon from unstable field structures based on the electromagnetic field to self-stabilized gravitomagnetic field structures.

“…Vishwakarma [12] observes that the conventional Kasner metric interpretation is "obscure and questionable". In [13] In [14] I prove that ( ) ( )…”

Section: The K N V-metric Theory-of-gravitymentioning

confidence: 99%

A Self-Stabilized Field Theory of Neutrinos

2021

JHEPGC

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In "A Self-linking Field Formalism" I establish a self-dual field structure with higher order self-induced symmetries that reinforce the first-order dynamics.The structure was derived from Gauss-linking integrals in 3 ℜ based on the Biot-Savart law and Ampere's law applied to Heaviside's equations, derived in strength-independent fashion in "Primordial Principle of Self-Interaction".The derivation involves Geometric Calculus, topology, and field equations. My goal in this paper is to derive the simplest solution of a self-stabilized solitonic structure and discuss this model of a neutrino.