OALibJ  Vol.2 No.10 , October 2015
On the Origin of Electric Charge
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Abstract: By starting from a quaternionic separable Hilbert space as a base model, the paper uses the capabilities and the restrictions of this model in order to investigate the origins of the electric charge and the electric fields. Also, other discrete properties such as color charge and spin are considered. The paper exploits all known aspects of the quaternionic number system and it uses quaternionic differential calculus rather than Maxwell based differential calculus. The paper presents fields as mostly continuous quaternionic functions. The electric field is compared with another basic field that acts as a background embedding continuum. The behavior of photons is used in order to investigate the long range behavior of these fields. The paper produces an algorithm that calculates the electric charge of elementary particles from the symmetry properties of their local parameter spaces. The paper also shows that the usual interpretation of a photon as an electric wave is not correct.
Cite this paper: van Leunen, J. (2015) On the Origin of Electric Charge. Open Access Library Journal, 2, 1-14. doi: 10.4236/oalib.1101836.

[1]   In 1843 quaternions were discovered by Rowan Hamilton.

[2]   Quantum logic was introduced by Garret Birkhoff and John von Neumann in their paper: Birkhoff, G. and von Neumann, J. (1936) The Logic of Quantum Mechanics. Annals of Mathematics, 37, 823-843.
This paper also indicates the relation between this orthomodular lattice and separable Hilbert spaces.

[3]   The Hilbert space was discovered in the first decades of the 20th century by David Hilbert and others.

[4]   In the sixties Israel Gelfand and GeorgyiShilov introduced a way to model continuums via an extension of the separable Hilbert space into a so called Gelfand triple. The Gelfand triple often gets the name rigged Hilbert space. It is a non-separable Hilbert space.

[5]   Paul Dirac introduced the braket notation, which popularized the usage of Hilbert spaces. Dirac also introduced its delta function, which is a generalized function. Spaces of generalized functions offered continuums before the Gelfand triple arrived.
See: Dirac, P.A.M. (1958) The Principles of Quantum Mechanics. 4th Edition, Oxford University Press, Oxford, ISBN 978 0 19 852011 5.

[6]   Quaternionic function theory and quaternionic Hilbert spaces are treated in: van Leunen, J.A.J. (2015) Quaternions and Hilbert Spaces. .

[7]   In the second half of the twentieth century Constantin Piron and Maria Pia Solèr proved that the number systems that a separable Hilbert space can use must be division rings. See: Baez, J. (2011) Division Algebras and Quantum Theory. and Holland, S.S. (1995) Orthomodularity in Infinite Dimensions: A Theorem of M. Solèr. Bulletin of the American Mathematical Society, 32, 205-234

[8]   van Leunen, J.A.J. (2015) Foundation of a Mathematical Model of Physical Reality.