Authors: J.A.J. van Leunen
By starting from an infinite dimensional quaternionic separable Hilbert space and its companion Gelfand triple as a base model, the paper uses the capabilities and the restrictions of this model in order to investigate the origins of some basic fields. A special method is introduced that generates normal operators and parameter spaces from existing quaternionic number systems. The same method is used to relate functions that use these parameter spaces with corresponding normal operators. Continuum eigenspaces of operators that reside in the Gelfand triple will represent the investigated basic fields. The paper exploits all known aspects of the quaternionic number system and it uses quaternionic differential calculus as well as Maxwell based differential calculus. This is done in order to investigate the properties and behavior of the investigated basic fields. The two toolkits offer different views on the basic fields. The views do not affect the behavior of the investigated field. Maxwell based differential calculus is commonly used to investigate the electromagnetic field, but the application of this set of equations is certainly not restricted to the EM field. The EM field is compared with another basic field that acts as a background embedding continuum. Both basic fields can be investigated by the Maxwell based equations and by the quaternion differential calculus. It will be shown that the fundamental difference between the basic fields is located in the artifacts that vibrate and deform these basic fields. The paper produces an algorithm that calculates the electric charge and color charge of elementary objects from the symmetry properties of their local parameter spaces. The electric charges generate the electric field. Also the spin of elementary objects is considered. Via the analysis of the Dirac equation the paper indicates that the wave equation is the result of the coupling between two first order differential equations that hold for different parameter spaces. The paper reveals that dedicated mechanism control the coherence of the dynamics of the fields. The behavior of photons and dynamic electromagnetic fields is used in order to investigate the long range behavior of these fields. The paper shows that the usual interpretation of a photon as an electric wave is not correct. In addition the relation between gravitation and inertia is explained.
Comments: 54 Pages.
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