From Osher Doctorow
We've seen that Quaternions may account for gravitation as well as
much of the rest of physics if a probabilistic (especially Probable
Influence/Causation) framework is used.
Two papers of the last few days in arXiv indicate that Quaternions are
far more versatile than is usually thought.
1) "Nonlinear Dirac operator and quaternionic analysis,", Andriy
Haydys, U. Bielefeld Germany, arXiv: 0706.0389 v1 [math.DG] 4 Jun
2007, 16 pages (based partly on his Dissertation).
2) "Quaternionic wave packets," Stefano De Leo and Gisele C. Ducati
(respectively U. Campinas and U of Pirana Brazil), arXiv: 0706.0228 v1
[mth.ph] 1 Jun 2007, 9 pages.
The second paper concludes that there is a qualitative difference
between complex and quaternionic quantum mechanics. The authors
continue their work from J. Phys A 2002, 2005, and 2006, and continue
the work of S. L. Adler's Quaternionic quantum mechanics and quantum
fields, Oxford U. Press: N.Y. and Oxford 1995.
The first paper generalizes Dirac operators and generalizes the
complex Cauchy-Riemann Equations (already partly generalized before)
to the Cauchy-Riemann-Fueter Equation and generalizes spinors and
finds a relationship between harmonic spinors of a generalized
nonlinear Dirac operators and solutions of that Cauchy-Riemann Fueter
Equation.
These papers come amidst (or rather, stand out against, in my view) on
onslaught of papers by LQG (Loop Quantum Gravity) people and by
logarithmic advocates in statistics. One of the logarithmic-
advocating papers is somewhat amusing since it proposes discovering a
logarithmic law relating to characteristic functions in probability-
statistics - apparently hoping that nobody will notice that
characteristic functions are by definition in exponential form.
Osher Doctorow
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