The SM finaly realized as particles w/o particle .

[MTd2]

The SM finaly realized as "particles w/o particle".

Robert Filnkelstein has been trying to find a whole description based on quantum knots. Today, he uploaded a paper in which he finally finds it. Although not cited in the article, these are extremely similar the field flux knots which Wilczec looked for.

http://arxiv.org/abs/0912.3552

 

[arivero]

Does anyone have the reference of the XIXth century work on knot theory as a way to classify the chemical atoms?

 

[MTd2]

Not a book, but a paper. This is a reference:

Thompson, W. T. "On Vortex Atoms." Philos. Mag. 34, 15-24, 1867.

And here's a link to the paper:

http://www.info.global-scaling-verein.de/Others/VortexAtoms.pdf

And a html version of it:

http://zapatopi.net/kelvin/papers/on_vortex_atoms.html

EDIT:

The above paper is the same one in the reference 1. It was just re edited and republished in a different magazine.

 

[marcus]

... Although not cited in the article, these are extremely similar the field flux knots which Wilczek looked for.
...

Can you help us locate the relevant journal article(s) by Wilczek?

btw I see the (December 2009) Finkelstein paper which you call attention to here has a link to an earlier (January 2009) Finkelstein paper. I'll check that to see if it has references to related work.
http://arxiv.org/abs/0901.1687
Colored Preons
Robert J. Finkelstein
10 pages, 4 Tables
(Submitted on 12 Jan 2009)
"Previous studies have suggested complementary models of the elementary particles as (a) quantum knots and (b) preonic nuclei that are field and particle descriptions, respectively, of the same particles. This earlier work, carried out in the context of standard electroweak (SU(2) x U(1)) physics, is here extended to the strong interactions by the introduction of color (SU(3)) charges."

No, unfortunately. The January paper only has 4 references, all to papers by Finkelstein. One of those cited is this:
http://arxiv.org/abs/0806.3105
Knots and Preons
Robert J. Finkelstein
12 pages; 4 tables
(Submitted on 18 Jun 2008)
"It is shown that the four trefoil solitons that are described by the irreducible representations D^3/2_mm' of the quantum algebra SL_q(2) (and that may be identified with the four families of elementary fermions (e,\mu,\tau;\nu_e\nu_\mu\nu_\tau;d,s,b;u,c,t) may be built out of three preons, chosen from two charged preons with charges (1/3,-1/3) and two neutral preons. These preons are Lorentz spinors and are described by the D^1/2_mm' representation of SL_q(2). There are also four bosonic preons described by the D¹_mm' and D⁰₀₀ representations of SL_q(2). The knotted standard theory may be replicated at the preon level and the conjectured particles are in principle indirectly observable."

Again, this June 2008 Finkelstein has very few references, only three, which are other Finkelsteins. The author does not seems to want to indicate how his work relates to that of other people.

It's curious. By contrast, Bilson-Thompson, in his 2005 braid preon paper http://arxiv.org/pdf/hep-ph/0503213 , went to some length to point out the relationship to earlier work. Subsequent braid matter papers by Sundance and others have done likewise. Robert Finkelstein appears exceptional in only citing his own work.

 

[MTd2]

Can you help us locate the relevant journal article(s) by Wilczek?

This is the one:

http://arxiv.org/abs/0812.5097

New Kinds of Quantum Statistics

Frank Wilczek
(Submitted on 30 Dec 2008 (v1), last revised 26 Jan 2009 (this version, v3))
I review the quantum kinematics of identical particles, which suggests new possibilities, beyond bosons and fermions, in 2+1 dimensions; and how simple flux-charge constructions embody the new possibilities, leading to both abelian and nonabelian anyons. I briefly allude to experimental realizations, and also advertise a spinor construction of nonabelian statistics, that has a 3+1 dimensional extension.

If you look else where, non abelian anyons are described by quantum groups, for example:

http://quantum.leeds.ac.uk/~phyjkp/TQC_Review.pdf

And notice that q-algebras, as Robert Finkelstein used, is a quantum group.


But it is indeed really weird that he didn't try to connect to other people. It wouldn't be that hard...