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Science Forum Index » Physics Forum » Quantum Gravity 273.6: Quantum Gravity, Jacobson...
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| OsherD... |
 Posted: Thu Jul 03, 2008 7:11 pm |
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From Osher Doctorow
We come back to Quantum Gravity through not only the Jacobson Radicals
but general Radicals of analogous or similar type, several of the
above words in the heading and others below mentioned in Victor S.
Shulman and Yuri V. Turovskii's May 2008 paper in arXiv (I omitted to
write down its arXiv number because the paper doesn't specifically
mention applications to physics). Some of the other keywords in
Shulman and Turovskii and others are:
1) topological radicals
2) spectral radius
3) radical operator algebras
4) joint spectral radius
5) Volterra semigroup
6) Volterra operators (compact quasinilpotent operators, forming a
semigroup)
7) Berger-Wang formula and its generalization
 Calkin algebra
9) Casimir operator (28 papers arXiv, including one in 2008; important
for symmetric groups for physical theories for classification schemes
and to thereby establish mass formulas).
This leads us to: "Casimir operators induced by Maurer-Cartan
equations," by Rutwig Campoamor-Stursberg, U. Complutense de Madrid
Spain, arXiv: 0805.2982 v1 [hep-th] 19 May 2008, 18 pages. Section
4.1 of this involves Lie algebras sa(N, R), the spectral affine
algebra which equals sl(n, R) +_R (right arrow over the circled +) nL1
appearing in quantum gauge theories of gravity.
Following up "Maurer-Cartan equations" as keywords in arXiv leads us
to 10 papers, 3 of which are in 2008, especially a paper by Francois
Gieres (who has 26 papers in arXiv) of U. de Leon France called
"Translation-invariant models for non-commutative gauge fields,"
Daniel N. Blascko, Francois Gieres, Erwin Kronberger, Manfed Schweb,
Michael Wohlgenannt, respectively Vienna U. Technology, U. Lyon,
Vienna U. Technology, Vienna U. Technology, and University of Vienna
Austria, arXiv: 0804.1914 v1 [hep-th] 11 Apr 2008, 9 pages.
Here they point out that noncommuting spacetime coordinates appear in
various approach to Quantum Gravity and refer to reviews of M.R.
Douglas and Nekrasov as well as R. J. Scabo, respectively arXiv: hep-
th/0106048 and 0109162, and they introduce models for noncommutative
U(1) gauge fields including extra terms into the action to get rid of
UV/IR mixing, and the gauge field propagator in the Landau gauge
reduces to a simple form with factor:
10) 1[k^2 + 1/k^2]
which Readers may recognize as the type of generator (of the
denominator) of the Golden Mean via:
11) x - 1/x - 1 = 0
or multiplying both sides by x:
12) x^2 - x - 1 = 0 (solution includes x = (1 + sqrt(5))/2, the Golden
Mean/Ratio)
Here k is a coefficient in the action.
The Golden Mean and Jacobson Radical have already been explained as
related to Probable Causation/Influence (PI) in recent and previous
posts.
Osher Doctorow |
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