If we can detect N = 4 SUSY quaternionic or 16 supersymmetries in the Clifford algebra CL_16, most likely in a broken symmetry phase, we would be in great shape! ❋ Unknown (2009)
We will focus on the 120, which are a representation of quaternionic fields. ❋ Sean (2008)
If the four manifold is a 4-sphere then the 3-homology sphere bounds both of then and there is then a quaternionic structure in the whole 4-space. ❋ Sean (2008)
Yet this strange configuration to the CMB might be a signature of the quaternionic structure of the universe in the inflationary or pre-inflationary phase. ❋ Sean (2008)
The Dirac equation is essentially the “square root” of the Klein-Gordon equation in a quaternionic form. ❋ Julianne (2008)
Unfortunately, the electrogravitational implications of Whittaker's profound work were not recognized and followed up, and their connection to Maxwell's quaternionic EM theory was not noticed nor examined. ❋ Unknown (1990)
With the availability of excellent and extensive expositions of the vector interpretation of the translation force-field subset of Maxwell's theory by Heaviside and Hertz, and with the nearly insurmountable difficulty associated with the complex quaternions and potentials which few scientists understood, the rejection of the quaternionic form of Maxwell's theory and the acceptance of the vector subset was inevitable. ❋ Unknown (1990)
Working engineers and leading scientists focused upon Heaviside's vector interpretation of Maxwell's difficult quaternionic expressions. ❋ Unknown (1990)
Maxwell's compact and powerful quaternionic expression of the general equations of the electromagnetic field are given in Article 619, Vol. 2, p. 258 of his Treatise. ❋ Unknown (1990)
● Piron's result: from elementary questions recover the geometry of the Hilbert space (over the reals, complex, and quaternionic numbers). ❋ Unknown (2009)
[1965] shows that a real, complex or quaternionic inner product space ❋ Unknown (2009)
Just how much more powerful was Maxwell's quaternionic expression of EM theory than was Heaviside's vector interpretation, was succinctly expressed by Josephs: "Hamilton's algebra of quaternions, unlike Heaviside's algebra of vectors, is not a mere abbreviated mode of expressing Cartesian analysis, but is an independent branch of mathematics with its own special rules of operation and its own special theorems. ❋ Unknown (1990)
11 - The Jordan algebra of nXn self-adjoined quaternionic matrices. ❋ Unknown (2009)
