On the Origin of Electric Charge

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References

[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