On the Origin of Electric Charge ()

Johannes Antonie Josephus van Leunen^{}

Retired Physicist.

**DOI: **10.4236/oalib.1101836
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Retired Physicist.

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.

Keywords

Quantum Physics, Mathematical Model, Electric Charge, Electric Field, Embedding Field, Photon, Wave Equation, Quaternionic Hilbert Space, Quaternionic Differential Calculus, Symmetry Flavor

Share and Cite:

van Leunen, J. (2015) On the Origin of Electric Charge. *Open Access Library Journal*, **2**, 1-14. doi: 10.4236/oalib.1101836.

Conflicts of Interest

The authors declare no conflicts of interest.

[1] |
In 1843 quaternions were discovered by Rowan Hamilton. http://en.wikipedia.org/wiki/History_of_quaternions |

[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. http://en.wikipedia.org/wiki/Hilbert_space. |

[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. http://www.encyclopediaofmath.org/index.php?title=Rigged_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. http://vixra.org/abs/1411.0178 . |

[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. http://arxiv.org/abs/1101.5690 and Holland, S.S. (1995) Orthomodularity in Infinite Dimensions: A Theorem of M. Solèr. Bulletin of the American Mathematical Society, 32, 205-234 http://www.ams.org/journals/bull/1995-32-02/S0273-0979-1995-00593-8/ |

[8] |
van Leunen, J.A.J. (2015) Foundation of a Mathematical Model of Physical Reality. http://vixra.org/abs/1502.0186 |

[9] | http://en.wikipedia.org/wiki/Yukawa_potential |

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